Googology Wiki - 用户贡献 [zh-cn]

FTO

2026-05-22T11:08:37Z

Baixie01000a7：/* 性质 */

'''FTO（First Transfinite Ordinal，第一个超限序数，即'''<math>\omega</math>'''）'''，是一个重要的[[序数]]。它被认为是具有“里程碑”意义的一个序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|<math>\varphi(1)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(0)</math>
|-
|[[初等序列系统|PrSS]]
|<math>0,1</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 \end{pmatrix}</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,2</math>
|-
|[[HPrSS]]
|<math>1,2</math>
|-
|[[0-Y]]
|<math>1,2</math>
|-
|[[Y序列|1-Y]]
|<math>1,2</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(1)</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(1)</math>
|}

=== 性质 ===
ω 是最小的[[序数#超限序数|超限序数]]，最小的非零[[序数#极限序数|极限序数]]，最小的不满足 <math>1+\alpha=\alpha+1</math> 的序数<math>\alpha</math>。

<math>\omega = |\omega| = \aleph_{0} </math>，详见[[基数]]。

[[证明论序数]]：<math>\rm Q</math>，<math>\rm KP^-</math>

极限在此处的记号：[[高德纳箭头]]，[[阿克曼函数]]，[[斯坦豪斯-莫泽表示法]]，[[下箭号表示法]]，[[Sudan 函数|苏丹函数]]，超运算

[[分类:序数]]

Googology 梗百科

2026-05-21T13:53:41Z

Baixie01000a7：/* 3.都在大群拉💩是吧？全都跑不了 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15后陆续出现“打断复读”、“打断打断复读”、“打断^ω 复读”、“ε(打断+1) 复读”、“2nd 复读”……

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)。

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

Loader 数

2026-05-15T17:43:47Z

Baixie01000a7：

'''Loader 数'''是 Ralph Loader 的 C 语言程序 '''Loader.c''' 的输出 <math>D^5(99)</math>，它在 2001 年的 [[Bignum Bakeoff]] 比赛（用不超过 512 字的代码生成尽可能大的有限整数）中获得第一名。

其中 D 函数的强度取决于 Huet-Coquand 构造演算（CoC）的证明论强度，其增长率达到了 <math>\mathrm {PTO}(\mathrm{Z}_\omega)</math>。迄今为止，它仍然是最强的可计算函数之一。

=== 定义 ===
Loader.c 的源代码<ref>https://github.com/rcls/busy</ref>如下：<syntaxhighlight lang="c" line="1">
#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T L X C
S (v+2, t U y C c, Z (X )))
:
A (T L X C
T Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B c = P d, c C
t U t C
u U u) )
C
c && B
t = P
~u & 2 | B
u = 1 <此外，Loader 还给出了可读性更高的版本（我们使用中文注释）：<syntaxhighlight lang="c">
//Tree、INT、TREE、BitStream 都被定义为 int，只是为了区分用途。
//把宏 DESCEND 直接展开为变量 xx，用于 while 里的递归控制。
typedef int Tree;
typedef int INT;
typedef int TREE;
typedef int BitStream;
#define DESCEND xx

// 全局临时变量：
// lastRight —— 用于在解码配对结构时暂存“另一半”值；
// accumulate —— 累积所有推导结果（每个结果是(term, type, 剩余比特流, context) 四元组的配对编码）。
Tree lastRight, accumulate;

// —— 基础编码：二元配对函数 ——
// 将两个非负整数 yy, xx 编码为一个整数，保证一一对应（双射）。
// 公式：Pair(yy,xx) = (yy − ~yy) << xx = (2*yy + 1) << xx
// 这样低位的连续零数目即为 xx，高位奇数部分即为 2*yy+1，方便快速解码。
TREE Pair (TREE yy, TREE xx)
{
return yy - ~yy << xx;
}

// —— 解码：取配对的第二个分量 ——
// 从编码值 xx 中恢复出原始的第二个参数（移位次数）。
// 逻辑：若 xx 为奇数，则移位次数为 0；否则不断除以 2 并累加，直到遇到奇数。
// 计算结果同时写入 lastRight。
TREE Right (TREE xx)
{
return lastRight = xx % 2 ? 0 : 1 + Right (xx / 2);
}

// —— 解码：取配对的第一个分量 ——
// 先将编码右移 1 位（去除最低位信息），再右移 Right(xx) 位，得到原始的 yy。
// 上一次调用 Right 时已经把移位计数存入 lastRight，因此这里可直接使用。
TREE Left (TREE xx)
{
return xx / 2 >> Right (xx);
}

// —— 宏：提升（Lift） ——
// 将所有自由变量的 De Bruijn 索引统一 +1，维护绑定层级。
// 通过 Subst(vv=4, yy=13, context=-4, term=xx) 实现。
#define Lift(xx) Subst (4, 13, -4, xx)

// —— 归一化替换（Subst） ——
// 在 term 中，将索引 vv 的变量替换为术语 yy，并对索引 > vv 的变量减去 context。
// 同时对 λ 抽象 (aux=0)、Π 构造 (aux=1) 和函数应用 (aux=2) 等节点进行递归归一化。
// 参数说明：
// vv : 要替换的变量索引
// yy : 用来替换的术语（已规范化）
// context : 替换后，所有更大索引变量需减去的偏移
// term : 待处理的术语编码
TREE Subst (INT vv, TREE yy, INT context, TREE term)
{
Tree aux = Left (term), // 当前节点类型：0=λ，1=Π，2=应用，>2=变量/常量
xx = lastRight; // 当前节点主体或子配对

// 按节点类型分支处理
if (aux == 2) {
// 应用节点：先递归替换，再用 Apply 做 β-归约或重构
return Apply (
Subst (vv, yy, context, Left (xx)),
Subst (vv, yy, context, Right (xx))
);
}
else if (aux > 2) {
// 变量或常量：
// 若 aux == vv，则替换为 yy；否则若 aux>vv，就减去偏移 context
return aux == vv
? yy
: term - (aux > vv ? context : 0);
}
else {
// 抽象节点：aux==0 为 λ，aux==1 为 Π
// 构造新配对 (aux, (子项1', 子项2'))
// 对右子树的 yy 先做 Lift 以调整绑定深度
return Pair (
aux,
Pair (
Subst (vv, yy, context, Left (xx)),
Subst (vv+2, Lift(yy), context, Right (xx))
)
);
}
}

// —— 函数应用归一化（Apply） ——
// 若 yy 的操作码 Left(yy)==1（λ 抽象），则对其主体做一次 β-归约：Subst(4, xx, 4, body)。
// 否则重构应用节点 Pair(2, Pair(yy, xx))。
TREE Apply (TREE yy, TREE xx)
{
return Left (yy) == 1
? Subst (4, xx, 4, Right (lastRight))
: Pair (2, Pair (yy, xx));
}

// —— 比特流测试宏 ——
// 把 xx 当作待消费的比特流，每用一次 xx/=2，测试被除后最低位是否为 1。
#define MAYBE (xx /= 2) % 2 &&

// —— 主推导过程（Derive） ——
// 将整数 xx 视作一条比特流，按照 Curry–Howard 同构/类型规则生成所有可能的 λ 术语并归一化。
// 输出的(term, type, 剩余比特流, context) 四元组不断累加到全局 accumulate 中。
// 算法概览：
// 1. 递归调用 Derive(xx-1)，保证对所有小于 xx 的比特串也进行推导，确保单调增长。
// 2. 在 while 循环中，依次用 MAYBE 消费一位比特，决定是否执行对应规则：
// - APPLY (函数应用 β-归约)
// - 弱化 (Weaken，将新假设压入上下文，并提升当前项/类型)
// - Π 构造 / λ 引入
// - 变量引入 (VAR(0))
// 3. 每次规则应用后，把当前 term/type/剩余比特流/context 打包配对累积。
TREE Derive (BitStream xx)
{
Tree aux, auxTerm;
Tree context = 0, // 初始空上下文
term = 7, // STAR 常量：Pair(3,0)=7
type = 14; // BOX 常量：Pair(3,1)=14

// while 条件中先递归 Derive(xx-1)，再根据下一位比特决定是否进入循环体
while (DESCEND && Derive (xx - 1), MAYBE (1)) {

// 1) 从子推导中获取一个新项 auxTerm 及其类型 aux
auxTerm = Left (Left (Derive (xx)));
aux = Left (lastRight);
xx = Left (lastRight); // 更新剩余比特流

// 2) 若当前上下文与子推导上下文相等，则可以尝试 APPLY 或 Weaken
if (context == lastRight) {
// — APPLY：当类型符合 Π(aux, -) 时，对 term 执行函数应用
if (Left (type) == 1 && Left (lastRight) == aux && MAYBE (1)) {
type = Subst (4, auxTerm, 4, lastRight);
term = Apply (term, auxTerm);
}
// — 弱化：若 auxType 是 STAR/BOX，可引入新假设
else if ((aux / 2) && MAYBE (1)) {
context = Pair (auxTerm, context);
term = Lift (term);
type = Lift (type);
}
}

// 3) Π 构造或 λ 引入：当上下文非空时，可根据比特选择
if (context && MAYBE (1)) {
// LHS：若 type 不支持 Π 构造，则强制做 λ 引入，并相应先对 type 做 Π 构造
Tree isLambda = (~type & 2);
if (MAYBE (isLambda)) {
type = Pair (1, Pair (Left (context), type)); // Π(Left(context), type)
}
term = Pair (isLambda | 0, Pair (Left (context), term));
context = lastRight; // 弹出已用的上下文项
}

// 4) 变量引入：若 type 是 STAR/BOX，可引入 VAR(0)
if ((type / 2) && MAYBE (1)) {
context = Pair (term, context);
type = Lift (term);
term = Pair (4, 0); // VAR(0)
}
}

// 将当前四元组打包，并加到 accumulate
return accumulate = Pair (
Pair (term, Pair (type, Pair (xx, context))),
accumulate
);
}

// —— 主函数 ——
// 对初值 99 连续调用五次 Derive，以充分“填充” accumulate。
TREE main ()
{
return Derive (Derive (Derive (Derive (Derive (99)))));
}
</syntaxhighlight>{{默认排序:相关问题}}
[[分类:记号]]

Loader 数

2026-05-15T17:43:30Z

Baixie01000a7：

'''Loader 数'''是 Ralph Loader 的 C 语言程序 '''Loader.c''' 的输出 <math>D^5(99)</math>，它在 2001 年的 [[Bignum Bakeoff]] 比赛（用不超过 512 字的代码生成尽可能大的有限整数）中获得第一名。

其中 D 函数的强度取决于 Huet-Coquand 构造演算（CoC）的证明论强度，其增长率达到了 <math>{\mathrm PTO}(\mathrm{Z}_\omega)</math>。迄今为止，它仍然是最强的可计算函数之一。

=== 定义 ===
Loader.c 的源代码<ref>https://github.com/rcls/busy</ref>如下：<syntaxhighlight lang="c" line="1">
#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T L X C
S (v+2, t U y C c, Z (X )))
:
A (T L X C
T Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B c = P d, c C
t U t C
u U u) )
C
c && B
t = P
~u & 2 | B
u = 1 <此外，Loader 还给出了可读性更高的版本（我们使用中文注释）：<syntaxhighlight lang="c">
//Tree、INT、TREE、BitStream 都被定义为 int，只是为了区分用途。
//把宏 DESCEND 直接展开为变量 xx，用于 while 里的递归控制。
typedef int Tree;
typedef int INT;
typedef int TREE;
typedef int BitStream;
#define DESCEND xx

// 全局临时变量：
// lastRight —— 用于在解码配对结构时暂存“另一半”值；
// accumulate —— 累积所有推导结果（每个结果是(term, type, 剩余比特流, context) 四元组的配对编码）。
Tree lastRight, accumulate;

// —— 基础编码：二元配对函数 ——
// 将两个非负整数 yy, xx 编码为一个整数，保证一一对应（双射）。
// 公式：Pair(yy,xx) = (yy − ~yy) << xx = (2*yy + 1) << xx
// 这样低位的连续零数目即为 xx，高位奇数部分即为 2*yy+1，方便快速解码。
TREE Pair (TREE yy, TREE xx)
{
return yy - ~yy << xx;
}

// —— 解码：取配对的第二个分量 ——
// 从编码值 xx 中恢复出原始的第二个参数（移位次数）。
// 逻辑：若 xx 为奇数，则移位次数为 0；否则不断除以 2 并累加，直到遇到奇数。
// 计算结果同时写入 lastRight。
TREE Right (TREE xx)
{
return lastRight = xx % 2 ? 0 : 1 + Right (xx / 2);
}

// —— 解码：取配对的第一个分量 ——
// 先将编码右移 1 位（去除最低位信息），再右移 Right(xx) 位，得到原始的 yy。
// 上一次调用 Right 时已经把移位计数存入 lastRight，因此这里可直接使用。
TREE Left (TREE xx)
{
return xx / 2 >> Right (xx);
}

// —— 宏：提升（Lift） ——
// 将所有自由变量的 De Bruijn 索引统一 +1，维护绑定层级。
// 通过 Subst(vv=4, yy=13, context=-4, term=xx) 实现。
#define Lift(xx) Subst (4, 13, -4, xx)

// —— 归一化替换（Subst） ——
// 在 term 中，将索引 vv 的变量替换为术语 yy，并对索引 > vv 的变量减去 context。
// 同时对 λ 抽象 (aux=0)、Π 构造 (aux=1) 和函数应用 (aux=2) 等节点进行递归归一化。
// 参数说明：
// vv : 要替换的变量索引
// yy : 用来替换的术语（已规范化）
// context : 替换后，所有更大索引变量需减去的偏移
// term : 待处理的术语编码
TREE Subst (INT vv, TREE yy, INT context, TREE term)
{
Tree aux = Left (term), // 当前节点类型：0=λ，1=Π，2=应用，>2=变量/常量
xx = lastRight; // 当前节点主体或子配对

// 按节点类型分支处理
if (aux == 2) {
// 应用节点：先递归替换，再用 Apply 做 β-归约或重构
return Apply (
Subst (vv, yy, context, Left (xx)),
Subst (vv, yy, context, Right (xx))
);
}
else if (aux > 2) {
// 变量或常量：
// 若 aux == vv，则替换为 yy；否则若 aux>vv，就减去偏移 context
return aux == vv
? yy
: term - (aux > vv ? context : 0);
}
else {
// 抽象节点：aux==0 为 λ，aux==1 为 Π
// 构造新配对 (aux, (子项1', 子项2'))
// 对右子树的 yy 先做 Lift 以调整绑定深度
return Pair (
aux,
Pair (
Subst (vv, yy, context, Left (xx)),
Subst (vv+2, Lift(yy), context, Right (xx))
)
);
}
}

// —— 函数应用归一化（Apply） ——
// 若 yy 的操作码 Left(yy)==1（λ 抽象），则对其主体做一次 β-归约：Subst(4, xx, 4, body)。
// 否则重构应用节点 Pair(2, Pair(yy, xx))。
TREE Apply (TREE yy, TREE xx)
{
return Left (yy) == 1
? Subst (4, xx, 4, Right (lastRight))
: Pair (2, Pair (yy, xx));
}

// —— 比特流测试宏 ——
// 把 xx 当作待消费的比特流，每用一次 xx/=2，测试被除后最低位是否为 1。
#define MAYBE (xx /= 2) % 2 &&

// —— 主推导过程（Derive） ——
// 将整数 xx 视作一条比特流，按照 Curry–Howard 同构/类型规则生成所有可能的 λ 术语并归一化。
// 输出的(term, type, 剩余比特流, context) 四元组不断累加到全局 accumulate 中。
// 算法概览：
// 1. 递归调用 Derive(xx-1)，保证对所有小于 xx 的比特串也进行推导，确保单调增长。
// 2. 在 while 循环中，依次用 MAYBE 消费一位比特，决定是否执行对应规则：
// - APPLY (函数应用 β-归约)
// - 弱化 (Weaken，将新假设压入上下文，并提升当前项/类型)
// - Π 构造 / λ 引入
// - 变量引入 (VAR(0))
// 3. 每次规则应用后，把当前 term/type/剩余比特流/context 打包配对累积。
TREE Derive (BitStream xx)
{
Tree aux, auxTerm;
Tree context = 0, // 初始空上下文
term = 7, // STAR 常量：Pair(3,0)=7
type = 14; // BOX 常量：Pair(3,1)=14

// while 条件中先递归 Derive(xx-1)，再根据下一位比特决定是否进入循环体
while (DESCEND && Derive (xx - 1), MAYBE (1)) {

// 1) 从子推导中获取一个新项 auxTerm 及其类型 aux
auxTerm = Left (Left (Derive (xx)));
aux = Left (lastRight);
xx = Left (lastRight); // 更新剩余比特流

// 2) 若当前上下文与子推导上下文相等，则可以尝试 APPLY 或 Weaken
if (context == lastRight) {
// — APPLY：当类型符合 Π(aux, -) 时，对 term 执行函数应用
if (Left (type) == 1 && Left (lastRight) == aux && MAYBE (1)) {
type = Subst (4, auxTerm, 4, lastRight);
term = Apply (term, auxTerm);
}
// — 弱化：若 auxType 是 STAR/BOX，可引入新假设
else if ((aux / 2) && MAYBE (1)) {
context = Pair (auxTerm, context);
term = Lift (term);
type = Lift (type);
}
}

// 3) Π 构造或 λ 引入：当上下文非空时，可根据比特选择
if (context && MAYBE (1)) {
// LHS：若 type 不支持 Π 构造，则强制做 λ 引入，并相应先对 type 做 Π 构造
Tree isLambda = (~type & 2);
if (MAYBE (isLambda)) {
type = Pair (1, Pair (Left (context), type)); // Π(Left(context), type)
}
term = Pair (isLambda | 0, Pair (Left (context), term));
context = lastRight; // 弹出已用的上下文项
}

// 4) 变量引入：若 type 是 STAR/BOX，可引入 VAR(0)
if ((type / 2) && MAYBE (1)) {
context = Pair (term, context);
type = Lift (term);
term = Pair (4, 0); // VAR(0)
}
}

// 将当前四元组打包，并加到 accumulate
return accumulate = Pair (
Pair (term, Pair (type, Pair (xx, context))),
accumulate
);
}

// —— 主函数 ——
// 对初值 99 连续调用五次 Derive，以充分“填充” accumulate。
TREE main ()
{
return Derive (Derive (Derive (Derive (Derive (99)))));
}
</syntaxhighlight>{{默认排序:相关问题}}
[[分类:记号]]

Goodstein函数

2026-05-15T17:20:47Z

Baixie01000a7：/* 枚举 */

'''古德斯坦函数(Goodstein Function)'''，是由鲁宾•古德斯坦(Reuben Goodstein)构造出的快速增长的函数。

== 定义 ==
首先需要定义数m的以n为底的遗传记法：

假设我们将一个非负整数m表示为n的幂次之和，然后将这些幂指数本身也表示为类似的幂次和，不断重复这一过程，直到所有的最高次指数都小于n。例如，我们可以将100写作<math>2^6+2^5+2^2</math>进一步可以写为<math>2^{2^2+2}+2^{2^2+1}+2^2</math>。这种表示方式称为m的以n为底的遗传记法。

Goodstein定义了一个数列<math>G_k(n)</math>：

对任意自然数n，都有<math>G_0(n)=n</math>

对任意自然数n,k，都有<math>G_{k+1}(n)</math>是把<math>G_k(n)</math>写成以k+2为底的遗传记法，随后把里面所有的k+2改成k+3，最后再把整个数减一所得到的数。

我们拿100作为例子：

<math>G_0(100) = 100 = 2^{2^2+2}+2^{2^2+1}+2^2</math>

<math>G_1(100) = 3^{3^3+3}+3^{3^3+1}+3^3-1 =3^{3^3+3}+3^{3^3+1}+3^2\times2+3\times2+2= 228767924549636</math>

<math>G_2(100) =4^{4^4+4}+4^{4^4+1}+4^2\times2+4\times2+1\approx3.486030062 \times 10^{156}</math>

……

这种快速增长的序列称为 Goodstein 序列。令人惊讶的是，对于 ''n'' 的所有值，<math>G_k(n)</math> 最终达到峰值、下降并返回零。这个事实被称为'''古德斯坦定理'''。更令人惊讶的是，可以证明古德斯坦定理无法用皮亚诺算术来证明。

我们定义古德斯坦函数<math>G(x)</math>等于古德斯坦序列<math>G_k(x)=0</math>时k的值。它的FGH增长率为<math>\varepsilon_0</math>.

== 例子 ==
我们以较小的x作为例子，来计算一下<math>G(x)</math>.为了更加清晰，我们不展示<math>G_k(n)</math> 的具体值，而是展示它的以k+2为底的遗传记法表示。读者可以自行计算取值。
{| class="wikitable mw-collapsible mw-collapsed" style="1"
|+x=1<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|1
|-
|1
|0
|}
因此G(1)=1.
{| class="wikitable mw-collapsible mw-collapsed"
|+x=2<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|2
|-
|1
|2
|-
|2
|1
|-
|3
|0
|}
因此G(2)=3.
{| class="wikitable mw-collapsible mw-collapsed"
|+x=3<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|2+1
|-
|1
|3
|-
|2
|3
|-
|3
|2
|-
|4
|1
|-
|5
|0
|}
因此G(3)=5.

从G(4)开始，古德斯坦函数将开始“起飞”
{| class="wikitable mw-collapsible mw-collapsed"
|+x=4<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|<math>2^2</math>
|-
|1
|<math>3^2\times2+3\times2+2</math>
|-
|2
|<math>4^2\times2+4\times2+1</math>
|-
|3
|<math>5^2\times2+5\times2</math>
|-
|4
|<math>6^2\times2+6+5</math>
|-
|9
|<math>11^2\times2+11</math>
|-
|10
|<math>12^2\times2+11</math>
|-
|21
|<math>23^2\times2</math>
|-
|22
|<math>24^2+24\times23+23</math>
|-
|45
|<math>47^2+47\times23</math>
|-
|46
|<math>48^2+48\times22+47</math>
|-
|93
|<math>95^2+95\times22</math>
|-
|189
|<math>191^2+191\times21</math>
|-
|381
|<math>383^2+383\times20</math>
|-
|402653181=<math>3\times2^{27}-3</math>
|<math>402653183^2</math>
|-
|402653182
|<math>402653184\times402653183+402653183</math>
|-
|<math>3\times2^{402653210}-3</math>
|<math>3\times2^{402653210}-1</math>
|-
|<math>3\times2^{402653210}-2</math>
|<math>3\times2^{402653210}-1</math>
|-
|<math>3\times2^{402653211}-3</math>
|0
|}
因此<math>G(4)=3\times2^{402653211}-3</math>

这里它展示了很清晰的“下降”过程。

我们有G(12)大于[[葛立恒数]]这个结论。

== 与 [[增长层级#哈代层级|HH]] 的关系 ==
定义<math>R^\omega_a(n)</math>为将n表示为以a为底的遗传记法，然后将所有的底数a全部替换为<math>\omega</math>所得到的序数。我们可以证明以下结论：

<math>G(n)=H_{R^\omega_2(n)}(3)-3</math>，其中<math>H_\alpha(n)</math>是 [[增长层级#哈代层级|Hardy 层级]]。

=== 证明 ===
以下叙述中总是考虑带乘法的[[康托范式]]和小于<math>\varepsilon_0</math>的序数，希腊字母表示序数，拉丁字母表示正整数。

先证一个引理：'''<math>H_{R^\omega_a(b+1)}(a)=H_{R^\omega_a(b)+1}(a)</math>，<math>a</math>是不小于3的正整数。'''

引理的证明：以下用<math>k</math>表示某个小于<math>a</math>的正整数。我们称一个序数<math>\alpha</math>是好的，如果它的康托范式中出现的所有正整数全都小于<math>a</math>。不难得出，<math>\alpha</math>是好的当且仅当它是某个<math>R^\omega_a(b)</math>的取值。

记<math>R^\omega_a(b+1)=\alpha</math>。将<math>H_\alpha(a)</math>进行多次取基本列，使下标为后继序数，得到<math>H_\beta(a)</math>。那么：

'''1) <math>\beta</math>是好的，不考虑正整数项。'''

由于<math>H_\beta(a)</math>的自变量为<math>a</math>，取基本列时得到的正整数不超过<math>a</math>。那么只要证明产生<math>\beta</math>时得到的<math>a</math>会在下一步被立即使用即可：

若<math>\alpha</math>是后继序数，则<math>\alpha=\beta</math>，显然是好的。

若<math>\alpha</math>是极限序数，设<math>\alpha=\alpha_0+\gamma\times{k}</math>：

# <math>\gamma=\omega</math>，则下一步得到<math>\alpha_0+\gamma\times{(k-1)}+a</math>，已经是后继了，故结论成立；
# <math>\gamma=\omega^{\delta+1}</math>，<math>\delta</math>是大于等于1的序数，则下一步得到<math>\alpha_0+\gamma\times{(k-1)}+\omega^\delta\times{a}</math>，下一步取<math>\omega^\delta\times{a}</math>的基本列，故结论成立；
# <math>\gamma=\omega^{\gamma_0+\omega\times{k}}</math>，则下一步得到<math>\alpha_0+\omega^{\gamma_0+\omega\times{(k-1)}+a}</math>，下一步取<math>\omega^{\cdots+a}</math>的基本列，故结论成立；
# <math>\gamma=\omega^{\gamma_0+\sigma\times{k}}</math>，<math>\sigma</math>是<math>\omega^2</math>的倍数，则此时等效于对<math>\sigma</math>取两次基本列的问题。由于<math>\sigma<\gamma</math>，使用序数的递降法知结论成立。

以上对于<math>\gamma=\omega^\sigma</math>中分别讨论了<math>\sigma=1</math>，<math>\sigma</math>为非1后继序数，<math>\sigma</math>为极限序数但不为<math>\omega^2</math>的倍数，<math>\sigma</math>为<math>\omega^2</math>的倍数的情况。综上，结论1)得证。

易得<math>g_{R^\omega_a(n)}(a)=n</math>，其中g是SGH。设<math>\beta=\theta+1</math>，则<math>\theta</math>是好的。所以，

由于增长层级在取基本列上规则相同，<math>g_\alpha(a)=g_\beta(a)</math>，

<math>g_{\theta+1}(a)=g_\beta(a)=g_\alpha(a)=b+1=g_{R^\omega_a(b)}(a)+1=g_{R^\omega_a(b)+1}(a)</math>，

<math>g_\theta(a)=g_{R^\omega_a(b)}(a)</math>。

由于<math>\theta</math>是好的，遗传记法是唯一的，故<math>\theta=R^\omega_a(b)</math>。从而<math>H_{R^\omega_a(b+1)}(a)=H_\alpha(a)=H_\beta(a)=H_{\theta+1}(a)=H_{R^\omega_a(b)+1}(a)</math>。引理得证。

'''原命题的证明''' 对于一般的自然数<math>k</math>，根据Goodstein序列的定义，有<math>R^\omega_{k+3}(G_{k+1}(n)+1)=R^\omega_{k+2}(G_k(n))</math>。于是，

<math>H_{R^\omega_{k+3}(G_{k+1}(n))}(k+4)=H_{R^\omega_{k+3}(G_{k+1}(n))+1}(k+3)</math>，

使用引理，

<math>=H_{R^\omega_{k+3}(G_{k+1}(n)+1)}(k+3)=H_{R^\omega_{k+2}(G_k(n))}(k+3)</math>。

于是，<math>H_{R^\omega_{k+2}(G_k(n))}(k+3)</math>是与<math>k</math>无关的常数。分别令<math>k=G(n)</math>，<math>k=0</math>，得到

<math>G(n)+3=H_0(G(n)+3)=H_{R^\omega_{G(n)+2}(0)}(G(n)+3)=H_{R^\omega_2(n)}(3)</math>，从而证明了

<math>G(n)=H_{R^\omega_2(n)}(3)-3</math>。

== 枚举 ==

有了刚刚的结论，我们可以快速地求出一些Goodstein函数的值。以下使用[[增长层级#快速增长层级|FGH]]，并且利用了结论<math>H_{\omega^\alpha}(n)=f_{\alpha}(n)</math>：

<math>G(0)=0</math>

<math>G(1)=1</math>

<math>G(2)=3</math>

<math>G(3)=5</math>

<math>G(4)=f_3(3)-3</math>

<math>G(5)=f_4(4)-3</math>

<math>G(6)=f_6(6)-3</math>

<math>G(7)=f_8(8)-3</math>

<math>G(8)=f_{\omega+1}(3)-3</math>

<math>G(9)=f_{\omega+1}(4)-3</math>

<math>G(10)=f_{\omega+1}(6)-3</math>

<math>G(11)=f_{\omega+1}(8)-3</math>

<math>G(12)=f_{\omega+1}(f_3(3))-3</math>

<math>G(13)=f_{\omega+1}(f_4(4))-3</math>

<math>G(14)=f_{\omega+1}(f_6(6))-3</math>

<math>G(15)=f_{\omega+1}(f_8(8))-3</math>

<math>G(16)=f_{\omega^3}(3)-3</math>

<math>G(17)=f_{\omega^4}(4)-3</math>

<math>G(18)=f_{\omega^6}(6)-3</math>

<math>G(19)=f_{\omega^8}(8)-3</math>

<math>G(20)=f_{\omega^\omega}(f_3(3))-3</math>

<math>\cdots</math>

一般地，我们有

<math>G(2\uparrow\uparrow{n})=f_{\omega\uparrow\uparrow(n-1)}(3)-3</math>。

据此可以得到，Goodstein函数的增长率为<math>\varepsilon_0</math>。

{{默认排序:相关问题}}
[[分类:记号]]

BMS

2026-05-15T11:12:15Z

Baixie01000a7：/* 争议 */

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto(Racheline)剽窃了他的证明。据test_alpha0所说，他在2022年2月16日在googology wiki上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline在ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

LRO

2026-05-15T11:06:38Z

Baixie01000a7：/* 性质 */

LRO（Large Rathjen Ordinal），是一个重要的序数，指代 <math>\rm{psd.}\omega.\rm{ply}-\rm{stb}</math> 折叠后的结果，其真实大小目前尚没有明确结论，主流的观点是 LRO=[[TSSO]]。另一个更常用的版本叫做 pfec.LRO（简称 pLRO），忽略 [[Σ1稳定序数#Non-Gandy 现象|Non-Gandy 现象]]，其大小等于 BMS(0)(1,1,1)(2,2,2)，这个序数又称 SBO（Small Bashicu Ordinal）或 OBO（Omega Back Ordinal）。<ref>BashicuHyudora (2015). バシク行列の解析 [Analysis of the Bashicu matrix]. ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E3%81%AE%E8%A7%A3%E6%9E%90</ref>
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\omega.\rm{ply}-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\alpha_\omega))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(C(1\{:\omega\}0))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,2)</math>
|-
|[[0-Y]]
|<math>1,4,10</math>
|-
|[[Y序列|1-Y]]
|<math>1,2,4,8,15</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p6))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\rm{BO})</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\Pi_2^1-\rm{CA}_0</math>，<math>\rm{KPnp}</math>（可能是 <math>\mathrm{KP}+\exist N \ \mathrm{admissibles-stable},N\in\omega</math> 的证明论序数<ref>HypCos (n.d.). TON vs. stability (remastered). ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/wiki/User:Hyp_cos/TON_vs._stability_(remastered)#Up_to_%CF%89_admissibles-stable</ref>）

极限在此处的记号：[[LMN]]，[[LON]]，non-recursive FGH，weak DLON，Lumi's LPSS，WDmEN，IUN，CCN，Sudden Hydra，[[Catching 函数|Catching Function]]，2-Proj，A Notation，1-Waiting Hydra

== 参考资料 ==
<references />
[[分类:序数]]

PPS

2026-05-09T14:06:36Z

Baixie01000a7：/* 改版+ PPS 4*/

'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。

PPS有着较为简单的定义，但分析它却极为复杂和困难。

2025年8月，PPS2被发现[[无穷降链]]。

2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。

2026年3月2日，PPS1的良序极限已被证实为<math>\zeta_0</math>。有关良序极限的一些解释，可以见[[用户:Phyrion/PPS|此处]]。

对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。

后续phyrion在25年圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。

前排提示：PPS的行为极其复杂，是标准的“果糕“记号

=== 定义 ===
以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。

PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）

极限表达式：0,1,2,3,4,5,......

记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x

展开：

1.如果末项是0，则它是后继序数

2.末项之前的部分保持不变

3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1

4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i>x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

5.基本列[n]为展开到第y+n*L-1项
=== 分析 ===
另见[[PPS分析]]

PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。

=== 地府段 ===
PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。

==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====
[[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]
0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。

它们分别对应序数<math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}</math>

和<math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}</math>。

几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。

==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====
0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。

不过，它已经被发现了无穷降链，或许这就是第二地府分析困难的原因。

=== 良序极限 ===
PPS的良序极限为

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,

3,0,21,19,

3,0,0,3,0,28,18,9,

3,0,33,30,9,

3,0,0,3,0,41,29,18,9,

3,0,47,43,18,9,

3,0,0,3,0,56,42,29,18,9,

3,0,63,58,29,18,9,

3,0,0,3,0,73,57,42,29,18,9,

3,0,81,75,42,29,18,9,

3,0,0,3,0,92,74,57,42,29,18,9,

3,0,101,94,57,42,29,18,9,

3,0,0,3,0,113,93,74,57,42,29,18,9,

3,0,123,115,74,57,42,29,18,9,

3,0,0,3,0,136,114,93,74,57,42,29,18,9,

3,0,147,138,93,74,57,42,29,18,9,

3,0,0,3,0,161,137,114,93,74,57,42,29,18,9,

3,0,173,163,114,93,74,57,42,29,18,9......

它的大小已被确定为ζ_0。

其基本列为：

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,18,9,3,0,26=ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,29,18,9,3,0,39=ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,42,29,18,9,3,0,54=ε_ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,43,18,9,3,0,0,3,0,56,42,29,18,9,3,0,63,57,42,29,18,9,3,0,71=ε_ε_ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,43,18,9,3,0,0,3,0,56,42,29,18,9,3,0,63,58,29,18,9,3,0,0,3,0,73,57,42,29,18,9,3,0,81,74,57,42,29,18,9,3,0,90=ε_ε_ε_ε_ε_ε_ε_ε_ε_ε_0

......

=== 改版 ===

==== PPM 1.2 ====
Parented Predecessor Matrix 1,2

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

==== PPM 2 ====
Parented Predecessor Matrix 2

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

其他项展开：对任意的i>y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

==== PPM 3 ====
Parented Predecessor Matrix 3

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：{

把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

}

末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项
==== PPS 4 ====
Parented Predecessor Sequence 4

极限表达式：0,1,2,3,....

坏根：列标是(末项的值)的项（首项的列标是1）；如果末项是0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b，末项的值为x、列标为y

末项展开：

> 如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么是弱展开，否则是强展开；
弱展开：将末项的值换成b；

> 强展开：在第b列和第x列(都不含)之间找到最右侧的值小于等于b的项，将末项的值换为这个项的列标；如果找不到，则等同弱展开

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

{{默认排序:序数记号}}
[[分类:记号]]

iBLP

2026-05-07T11:56:21Z

Baixie01000a7：/* 分析 */

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5)1，对应ω-Y极限。
{| class="wikitable"
|+
!ω-Y序列
!iBLP
|-
|1,2
|(1,0)1(2,1)1
|-
|1,2,4
|(1,0)1(2,1,0)1
|-
|1,2,4,8
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3
|-
|1,2,4,8,16
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4
|-
|1,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|-
|1,3,4,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|-
|1,3,7
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*9,*8,5,4,3,2,1,0)5
|-
|1,3,9
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*10,*9,*8,5,4,3,2,1,0)5
|-
|1,3,10
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,4)1
|-
|1,4
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2
|-
|1,5
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,4,3,2)2
|-
|1,6
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,4,3,2)2(7,4,3,2)2
|-
|Limit
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5)1
|}

{{默认排序:序数记号}}
[[分类:记号]]

序数超运算

2026-05-04T06:59:32Z

Baixie01000a7：

序数超运算是对序数使用[[超运算序列|超运算]]的尝试。它虽然是最直观、新人最容易想到的模式，但已经被长期的[[Googology]]实践所证明是低效、难以扩展的。

== 原定义 ==
首先，我们仿照[[高德纳箭头]]在自然数上的定义和[[序数#序数的运算|序数运算]]的定义，给出序数使用高德纳箭头的定义：

# <math>\alpha\uparrow^1\beta=\alpha^{\beta}</math>
# <math>\alpha\uparrow^c1=\alpha</math>
# <math>\alpha\uparrow^{c+1}(\beta+1)=\alpha\uparrow^c(\alpha\uparrow^{c+1}\beta)</math>
# <math>\alpha\uparrow^c\lambda=\sup\{\alpha\uparrow^c\beta|\beta<\lambda\}</math>

其中<math>\alpha,\beta</math>是任意序数，c是自然数，<math>\lambda</math>是非0极限序数。

这样一来，就有<math>\omega\uparrow^2(\omega+1)=\omega^{\omega\uparrow^2\omega}=\sup\{\omega^{\omega\uparrow^2n}|n<\omega\}=\sup\{\omega\uparrow^2n|n<\omega\}=\omega\uparrow^2\omega</math>.进一步，对任意<math>\beta\geq\omega</math>，都有<math>\omega\uparrow^2\beta=\omega\uparrow^2\omega</math>.再进一步，对任意的<math>c\geq2,\beta\geq\omega</math>,都有<math>\omega\uparrow^c\beta=\omega\uparrow^2\omega</math>.

这显然不是我们所期待的。

== 左结合法 ==
第一种试图解决问题的方案是左结合法。它借鉴了[[下箭号表示法|下箭头表示法]]，给出序数使用下箭头的定义：

# <math>\alpha\downarrow^1\beta=\alpha^{\beta}</math>
# <math>\alpha\downarrow^c1=\alpha</math>
# <math>\alpha\downarrow^{c+1}(\beta+1)=(\alpha\downarrow^{c+1}\beta)\downarrow\alpha</math>
# <math>\alpha\downarrow^c\lambda=\sup\{\alpha\downarrow^c\beta|\beta<\lambda\}</math>

其中<math>\alpha,\beta</math>是任意序数，c是自然数，<math>\lambda</math>是非0极限序数。

于是有：

<math>\omega\downarrow^22=\omega^\omega
</math>

<math>\omega\downarrow^23=\omega^{\omega^2}</math>

<math>\omega\downarrow^2\omega=\omega^{\omega^\omega}</math>

<math>(\omega\downarrow^2\omega)\downarrow^22=\omega^{\omega^{\omega^\omega}}</math>

<math>\omega\downarrow^33=\omega^{\omega^{\omega^{\omega^\omega}}}</math>

<math>\omega\downarrow^34=\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}</math>

<math>\omega\downarrow^3\omega=\varepsilon_0</math>

<math>(\omega\downarrow^3\omega)\downarrow^22=\varepsilon_0^{\varepsilon_0}</math>

<math>(\omega\downarrow^3\omega)\downarrow^2\omega=\varepsilon_0^{\varepsilon_0^\omega}</math>

<math>(\omega\downarrow^3\omega)\downarrow^32=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}</math>

<math>(\omega\downarrow^3\omega)\downarrow^33=\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}</math>

<math>\omega\downarrow^43=\varepsilon_1</math>

<math>\omega\downarrow^44=\varepsilon_2</math>

<math>\omega\downarrow^4\omega=\varepsilon_\omega</math>

<math>(\omega\downarrow^4\omega)\downarrow^3\omega=\varepsilon_{\omega+1}</math>

<math>(\omega\downarrow^4\omega)\downarrow^42=\varepsilon_{\varepsilon_\omega}</math>

<math>(\omega\downarrow^4\omega)\downarrow^43=\varepsilon_{\varepsilon_\omega2}</math>

<math>\omega\downarrow^53=\varepsilon_{\varepsilon_\omega\omega}</math>

<math>\omega\downarrow^54=\varepsilon_{\varepsilon_{\varepsilon_\omega\omega}\omega}</math>

<math>\omega\downarrow^5\omega=\zeta_0</math>

<math>\omega\downarrow^6\omega=\zeta_\omega</math>

<math>\omega\downarrow^7\omega=\varphi(3,0)</math>

<math>\omega\downarrow^{1+2n}\omega=\varphi(n,0)</math>

把下箭头用到序数上，其极限为<math>\varphi(\omega,0)</math>，也符合箭头运算的强度。

但是，左结合的下箭头行为和高德纳箭头差异还是不小，而且两个箭头对应一个<math>\varphi(n,0)</math>还是不太符合我们的预期。

== 攀爬法 ==
第二种试图解决问题的方案是攀爬法。攀爬法提供了一种更强的推广。我们知道，<math>\varepsilon_1</math>的基本列是<math>\{\varepsilon_0+1,\omega^{\varepsilon_0+1},\omega^{\omega^{\varepsilon_0+1}},\omega^{\omega^{\omega^{\varepsilon_0+1}}},\cdots\}</math>，我们可以将其表示为<math>\{\omega^{\omega^{\omega^{\cdots}}}+1,\omega^{\omega^{\omega^{\cdots}}+1},\omega^{\omega^{\omega^{\cdots}+1}},\cdots\}</math>.在这里我们把<math>\omega</math>的指数塔固定在<math>\omega</math>。在这样的基本列中，+1像在指数塔攀爬一样，攀爬法也因此而得名。在基本列的尽头，+1攀爬到了指数塔的顶端，与原来在顶端的1相加变为2。因此我们得到<math>\varepsilon_1=\underbrace{\omega^{\omega^{\cdots^{2}}}}_{\omega+1 \text{ layers}}</math>.进一步的，按照攀爬法我们有<math>\varepsilon_{\omega}=\underbrace{\omega^{\omega^{\cdots^{\omega}}}}_{\omega+1 \text{ layers}}</math>,我们将其记为<math>\omega\uparrow\uparrow(\omega+1)=\varepsilon_{\omega}</math>.

进一步有：

<math>\omega\uparrow\uparrow(\omega+2)=\varepsilon_{\omega^{\omega}}</math>

<math>\omega\uparrow\uparrow(\omega\times2)=\varepsilon_{\varepsilon_0}</math>

<math>\omega\uparrow\uparrow(\omega^2)=\zeta_0</math>

<math>\omega\uparrow\uparrow(\omega^3)=\eta_0</math>

<math>\omega\uparrow\uparrow(\omega^{\omega})=\varphi(\omega,0)</math>

<math>\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varphi(\varphi(1,0),0)</math>

<math>\omega\uparrow^34=\varphi(\varphi(\varphi(1,0),0),0)</math>

<math>\omega\uparrow^3\omega=\varphi(1,0,0)</math>

<math>\omega\uparrow^3(\omega+1)=\varphi(1,0,1)</math>

<math>\omega\uparrow^3(\omega^2)=\varphi(1,1,0)</math>

<math>\omega\uparrow^3\omega\uparrow^3\omega=\varphi(1,\varphi(1,0,0),0)</math>

<math>\omega\uparrow^44=\varphi(1,\varphi(1,\varphi(1,0,0),0),0)</math>

<math>\omega\uparrow^4\omega=\varphi(2,0,0)</math>

<math>\omega\uparrow^5\omega=\varphi(3,0,0)</math>

<math>\omega\uparrow^{\omega}\omega=\varphi(\omega,0,0)</math>

由此我们得到了攀爬法序数超运算的极限是<math>\varphi(\omega,0,0)</math>.

但是现在已经证明了，攀爬法是非良序的。因此这一做法得到的推广是不可靠的。

== +1法 ==
第三中试图解决问题的方案是+1法。

它基于一种特别朴素的想法，即：如果<math>\omega\uparrow^c\alpha=\alpha</math>,则修改其值为<math>\omega\uparrow^c(\alpha+1)</math>.显然，这一改变真正起到效果的是指数上的变化。当然，类似+1法，还可以用其他函数跳过不动点，例如+ω法，×2法，×ω法等，但不能达到下一个ε点。

关于+1法序数超运算，我们有：

例如：ω^^(ω+1)如果展开为ω^ω^^ω就会遇到不动点，因此触发上述的+1规则。

<math>\omega\uparrow\uparrow(\omega+1)=\omega^{\omega\uparrow\uparrow\omega+1}=\omega^{\varepsilon_0+1}</math>

然后，以此类推：

<math>\omega\uparrow\uparrow(\omega+2)=\omega^{\omega^{\varepsilon_0+1}}</math>

<math>\omega\uparrow\uparrow(\omega2)=\varepsilon_1</math>

<math>\omega\uparrow\uparrow(\omega3)=\varepsilon_2</math>

<math>\omega\uparrow\uparrow(\omega^2)=\varepsilon_{\omega}</math>

<math>\omega\uparrow^33=\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varepsilon_{\varepsilon_0}</math>

<math>\omega\uparrow^3\omega=\zeta_0</math>

到ζ_0后，+1法的展开方式将会比较复杂，并产生一些奇特的基础序列。继续分析：

<math>\omega\uparrow^3(\omega+1)=\omega\uparrow\uparrow(\omega\uparrow^3\omega+1)
=\omega\uparrow(\omega\uparrow\uparrow(\omega\uparrow^3\omega)+1)
=\omega\uparrow(\omega\uparrow^3\omega+1)
=\omega^{\zeta_0+1}</math>

<math>\omega\uparrow\uparrow(\omega\uparrow^3\omega+\omega)=\varepsilon_{\zeta_0+1}</math>

<math>\omega\uparrow\uparrow(\omega\uparrow^3\omega*2)=\varepsilon_{\zeta_02}</math>

<math>\omega\uparrow^3(\omega+2)=\omega\uparrow\uparrow(\omega\uparrow^3(\omega+1))=\varepsilon_{\omega^{\zeta_0+1}}</math>

<math>\omega\uparrow^3(\omega+3)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}</math>

<math>\omega\uparrow^3(\omega2)=\zeta_1</math>

<math>\omega\uparrow^43=\zeta_{\zeta_0}</math>

<math>\omega\uparrow^4\omega=\eta_0</math>

<math>\omega\uparrow^4(\omega+1)=\omega\uparrow^3(\omega\uparrow^4\omega+1)
=\omega\uparrow\omega\uparrow\uparrow\omega\uparrow^3(\omega\uparrow^4\omega+1)
=\omega\uparrow(\omega\uparrow^4\omega+1)
=\omega^{\eta_0+1}</math>

<math>\omega\uparrow^4(\omega+2)=\omega\uparrow^3(\omega\uparrow^4(\omega+1))=\zeta_{\omega^{\eta_0+1}}</math>

<math>\omega\uparrow^4(\omega2)=\eta_1</math>

<math>\omega\uparrow^5\omega=\varphi(4,0)</math>

<math>\omega\uparrow^{\omega}\omega=\varphi(\omega,0)</math>

于是我们得到其极限为<math>\varphi(\omega,0)</math>。它的优点是它和<math>\varphi</math>函数行为完全一致。但缺点也是这个。这导致了<math>\omega\uparrow\uparrow(\omega+1)=(\omega\uparrow\uparrow\omega)\times\omega</math>这种奇异的结果，某种意义上丢失了超运算自己的特性。因此可以说，+1法序数超运算被<math>\varphi</math>函数上位替代了。+1法序数超运算还可以继续拓展，在某些版本中，其增长率与类似的Veblen 函数及Feferman序数折叠函数类似，例如：

<math>\omega\{\omega\}(\omega2)=\varphi(\omega,1)</math>

<math>\omega\{\omega+1\}\omega=\varphi(\omega+1,0)</math>

<math>\omega\{\omega\uparrow\uparrow\omega\}\omega=\varphi(\varepsilon_0,0)</math>

<math>\omega\{\Omega\}3=\omega\{\omega\{\omega\}\omega\}\omega=\varphi(\varphi(\omega,0),0)</math>

<math>\omega\{\Omega\}\omega=\Gamma_0</math>

<math>\omega\{\Omega+1\}\omega=\varphi(1,1,0)</math>

<math>\omega\{\Omega2\}\omega=\varphi(2,0,0)</math>

<math>\omega\{\Omega^2\}\omega=\varphi(1,0,0,0)</math>

<math>\omega\{\Omega^\omega\}\omega=\psi(\Omega^{\Omega^\omega})</math>

<math>\omega\{\Omega^\Omega\}\omega=\psi(\Omega^{\Omega^\Omega})</math>

<math>\omega\{\Omega\uparrow\uparrow\omega\}\omega=\psi(\Omega_2)</math>

但如此的拓展达到同样序数的难度要明显大于一般的[[序数坍缩函数]]。有些版本引入了更为强大的结构，但已经失去了超运算的特性，其强度主要为引入的更高级序数结构，建议使用以更高级核心的序数记号替代之。

类似+1法的+ω法序数超运算由于整度较大，容易分析，方便进行拓展，有如下分析：[[+ω法序数超运算分析]]

== 总结 ==
到目前为止，序数超运算不是不良定义，就是不理想的。我们不建议在任何地方使用高于<math>\varepsilon_0</math>的序数超运算和更高级别的运算。如果要使用，必须仅仅将它作为形式上的符号，并且明确地说明其具体含义。事实上，我们完全可以使用[[Veblen 函数]]这样的更加强大且清晰的[[序数记号]]来替代它。
[[分类:记号]]
[[分类:入门]]
[[分类:序数超运算]]

Googology 梗百科

2026-05-01T14:40:19Z

Baixie01000a7：/* 3.都在大群拉💩是吧？全都跑不了 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15流光发送”打断复读“，随后出现“打断打断复读”，“打断^ω 复读”，“ε(打断+1) 复读”，“2nd 复读”……

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)。

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

Googology 梗百科

2026-05-01T14:39:45Z

Baixie01000a7：/* 一、聊天记录类 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15流光发送”打断复读“，随后出现“打断打断复读”，“打断^ω 复读”，“ε(打断+1) 复读”，“2nd 复读”……。

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

文件:nigancuangaiwodehua.jpg

2026-05-01T14:38:40Z

Baixie01000a7：

文件:lashit.jpg

2026-05-01T14:34:28Z

Baixie01000a7：

BOCF

2026-05-01T12:43:03Z

Baixie01000a7：重定向页面至序数坍缩函数

#重定向 [[序数坍缩函数]]

IBLP分析

2026-04-30T16:33:43Z

Baixie01000a7：创建页面，内容为“== Part 1: 0~ψ(Ω_ω*Ω) == 主词条：IBLP分析Part1 == Part 2: ψ(Ω_ω*Ω)~SHO == 主词条：IBLP分析Part2 == Part 3: SHO~Y(1,3,4,3) == 主词条：IBLP分析Part3”

== Part 1: 0~ψ(Ω_ω*Ω) ==
主词条：[[IBLP分析Part1]]

== Part 2: ψ(Ω_ω*Ω)~[[SHO]] ==
主词条：[[IBLP分析Part2]]

== Part 3: SHO~Y(1,3,4,3) ==
主词条：[[IBLP分析Part3]]

IBLP分析Part4

2026-04-30T16:30:36Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1
|1,3,4,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1
|1,3,4,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1
|1,3,4,3,4,2,5,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1(27,26)1
|1,3,4,3,4,2,5,9,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2)1
|1,3,4,3,4,2,5,9,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3
|1,3,4,3,4,2,5,9,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,3,4,2,5,9,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,2,1,0)3(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,12)1
|1,3,4,3,4,2,5,9,5,7,10
|-
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|1,3,4,3,4,2,5,9,5,7,10,5
|-
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|1,3,4,3,4,2,5,9,5,7,10,13
|-
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|1,3,4,3,4,2,5,9,5,7,10,14
|-
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|1,3,4,3,4,2,5,9,5,7,11
|-
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|1,3,4,3,4,2,5,9,5,7,12
|-
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|1,3,4,3,4,2,5,9,5,7,12,16,25
|-
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|1,3,4,3,4,2,5,9,5,7,12,17
|-
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|1,3,4,3,4,2,5,9,5,7,12,17,22
|-
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|1,3,4,3,4,2,5,9,5,7,12,18
|-
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|1,3,4,3,4,2,5,9,5,7,12,18,5
|-
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|1,3,4,3,4,2,5,9,5,7,12,19
|-
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|1,3,4,3,4,2,5,9,5,7,12,21,12
|-
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|1,3,4,3,4,2,5,9,5,8
|-
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|1,3,4,3,4,2,5,9,5,8,11
|-
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|1,3,4,3,4,2,5,9,5,9
|-
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|1,3,4,3,4,2,5,9,5,9,4,9,18,9,16
|-
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|1,3,4,3,4,3
|-
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|1,3,4,4
|-
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|1,3,4,4,2,5,9,5
|-
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|1,3,4,4,2,5,9,6
|-
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|1,3,4,4,2,5,9,6,5
|-
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|1,3,4,4,2,5,9,7
|-
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|1,3,4,4,2,5,9,7,10,5
|-
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|1,3,4,4,2,5,9,7,11
|-
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|1,3,4,4,2,5,9,7,12
|-
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|1,3,4,4,2,5,9,8
|-
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|1,3,4,4,2,5,9,8,11
|-
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|1,3,4,4,2,5,9,8,12
|-
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|1,3,4,4,2,5,9,8,12,4,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,9
|-
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|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,19
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,8,17
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,26
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,29
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,21
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,23
|-
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|1,3,4,4,2,5,9,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,8
|-
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|1,3,4,4,2,5,9,8,12,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,9
|-
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|1,3,4,4,2,5,9,8,12,10
|-
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|1,3,4,4,2,5,9,8,12,11
|-
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|1,3,4,4,2,5,9,8,12,11,15
|-
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|1,3,4,4,2,5,9,8,12,11,15,5
|-
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|1,3,4,4,2,5,9,8,12,11,15,12
|-
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|1,3,4,4,2,5,9,8,12,11,15,14,18
|-
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|1,3,4,4,2,5,9,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,15
|-
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|1,3,4,4,2,5,9,9,4,9,18,15,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,16
|-
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|1,3,4,4,2,5,9,9,4,9,18,18
|-
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|1,3,4,4,3
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|1,3,4,4,3,4,4,3
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|1,3,4,4,4
|-
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|1,3,4,4,4,2,5,9,9,6,5
|-
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|1,3,4,4,4,2,5,9,9,9
|-
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|1,3,4,4,4,2,5,9,9,9,4,9,18,18,16
|-
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|1,3,4,4,4,3
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|1,3,4,5
|-
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|1,3,4,5,2,5,9,10
|-
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|1,3,4,5,2,5,9,10,5
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|1,3,4,5,2,5,9,10,7
|-
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|1,3,4,5,2,5,9,10,8
|-
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|1,3,4,5,2,5,9,10,8,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,13
|-
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|1,3,4,5,2,5,9,10,8,12,13,11,15,16,14,18,19
|-
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|1,3,4,5,2,5,9,10,9
|-
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|1,3,4,5,2,5,9,10,9,5
|-
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|1,3,4,5,2,5,9,10,10
|-
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|1,3,4,5,2,5,9,10,13
|-
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|1,3,4,5,2,5,9,11
|-
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|1,3,4,5,2,5,9,11,16
|-
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|1,3,4,5,2,5,9,11,16,22
|-
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|1,3,4,5,2,5,9,11,16,25,16
|-
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|1,3,4,5,2,5,9,11,16,25,27
|-
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|1,3,4,5,2,5,9,11,16,25,29
|-
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|1,3,4,5,2,5,9,12
|-
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|1,3,4,5,2,5,9,12,15
|-
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|1,3,4,5,2,5,9,12,16
|-
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|1,3,4,5,2,5,9,12,16,5
|-
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|1,3,4,5,2,5,9,12,16,16
|-
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|1,3,4,5,2,5,9,12,16,16,5
|-
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|1,3,4,5,2,5,9,12,16,19
|-
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|1,3,4,5,2,5,9,12,16,19,23,5
|-
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|1,3,4,5,2,5,9,13
|-
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|1,3,4,5,2,5,9,13,17
|-
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|1,3,4,5,2,5,9,14
|-
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|1,3,4,5,2,5,9,14,4,9,18,28
|-
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|1,3,4,5,2,5,9,14,4,9,18,28,9
|-
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|1,3,4,5,2,5,9,14,4,9,18,29
|-
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|1,3,4,5,3
|-
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|1,3,4,5,4
|-
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|1,3,4,5,4,2,5,9,14,6,5
|-
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|1,3,4,5,4,2,5,9,14,9
|-
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|1,3,4,5,4,2,5,9,14,9,4,9,18,32,16
|-
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|1,3,4,5,4,3
|-
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|1,3,4,5,4,5
|-
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|1,3,4,5,4,5,2,5,9,14,9,10,5
|-
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|1,3,4,5,4,5,2,5,9,14,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,17,16)1
|1,3,4,5,4,5,2,5,9,14,9,14
|-
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|1,3,4,5,4,5,2,5,9,14,9,14,4,9,18,32,18,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,3,2,1,0)4(19,3,2)1
|1,3,4,5,4,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11)1
|1,3,4,5,5
|-
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|1,3,4,5,5,2,5,9,14,10,5
|-
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|1,3,4,5,5,2,5,9,14,11
|-
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|1,3,4,5,5,2,5,9,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2(16,15,11,8,5)2(17,16,15)1
|1,3,4,5,5,2,5,9,14,13,18
|-
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|1,3,4,5,5,2,5,9,14,13,18,5
|-
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|1,3,4,5,5,2,5,9,14,13,18,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,5
|-
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|1,3,4,5,5,2,5,9,14,13,18,17,22,21,26,5
|-
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|1,3,4,5,5,2,5,9,14,14
|-
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|1,3,4,5,5,3
|-
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|1,3,4,5,6
|-
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|1,3,4,5,6,2,5,9,14,15,5
|-
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|1,3,4,5,6,2,5,9,14,16
|-
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|1,3,4,5,6,2,5,9,14,17
|-
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|1,3,4,5,6,2,5,9,14,18
|-
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|1,3,4,5,6,2,5,9,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,5,6,2,5,9,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,5,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3
|1,3,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,3,2)1
|1,3,4,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,3,2)1
|1,3,4,6,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,15,8,5)3
|1,3,4,6,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1
|1,3,4,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1(16,3,2)1
|1,3,4,6,5,2,5,9,15,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2
|1,3,4,6,5,2,5,9,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,16,15)1
|1,3,4,6,5,2,5,9,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,*16,15,3,2,1,0)4(19,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2
|1,3,4,6,5,2,5,9,15,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3
|1,3,4,6,5,2,5,9,15,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2
|1,3,4,6,5,2,5,9,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,6,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,23,22,21)3
|1,3,4,6,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,6,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1
|1,3,4,6,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1(16,3,2)1
|1,3,4,6,7,2,5,9,15,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3
|1,3,4,6,7,2,5,9,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3(16,*15,12,3,2,1,0)4(17,*16,*15,12,4,3,2,1,0)5
|1,3,4,6,7,2,5,9,15,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,15,13)1
|1,3,4,6,7,2,5,9,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,3,2)1
|1,3,4,6,7,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,3,2,1,0)4(21,3,2)1
|1,3,4,6,7,8,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,17,15,13)3
|1,3,4,6,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,12,11,8,5)4
|1,3,4,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,16,15,13)2(18,17,16,15,13)3(19,*18,17,16,15,13)3
|1,3,4,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*16,*15,13,12,11,8,5)4
|1,3,4,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1
|1,3,4,7
|-
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|1,3,4,7,7
|-
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|1,3,4,7,8
|-
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|1,3,4,7,8,2,5,9,16,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2)1
|1,3,4,7,8,2,5,9,16,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,7,8,2,5,9,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,*15,*14,13,4,3,2,1,0)5
|1,3,4,7,8,2,5,9,16,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3
|1,3,4,7,8,2,5,9,16,20
|-
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|1,3,4,7,8,2,5,9,16,20,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1
|1,3,4,7,8,2,5,9,16,20,4,9,18,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1(26,25,2,1,0)3(27,*26,25,15,2,1,0)4(28,*27,26,25,16,15,2,1,0)5
|1,3,4,7,8,2,5,9,16,20,4,9,18,34,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1(26,25,23,20,17)3
|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,8,17,35,69,79
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,9
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,41
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42,54,73
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,3,2,1,0)3(16,*15,3,2,1,0)3(17,15,3)1(18,17,2,1,0)3(19,*18,17,3,2,1,0)4(20,*19,*18,17,15,3,2,1,0)5(21,*20,*19,*18,17,15,3,2,1,0)5(22,18,2,1,0)3(23,*22,18,3,2,1,0)4(24,*23,*22,18,15,3,2,1,0)5(25,*24,*23,18,17,15,3,2,1,0)6(26,*23,*22,18,15,3,2,1,0)5(27,26,23,22,18)3(28,*27,26,23,22,18)3(29,27,26)1(30,29,23,22,18)3(31,*30,29,26,23,22,18)4
|1,3,4,7,8,2,5,9,16,20,4,9,18,34,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,3,2)1
|1,3,4,7,8,2,5,9,16,20,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,8,5)1
|1,3,4,7,8,2,5,9,16,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*8,5,3,2,1,0)4
|1,3,4,7,8,2,5,9,16,20,9,4,9,18,34,43,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*8,5,3,2,1,0)4(16,3,2)1
|1,3,4,7,8,2,5,9,16,20,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15)1(18,17,15,8,5)3
|1,3,4,7,8,2,5,9,16,20,9,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,2,1,0)3(16,*15,11,3,2,1,0)4(17,*16,*15,11,4,3,2,1,0)5
|1,3,4,7,8,2,5,9,16,20,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2
|1,3,4,7,8,2,5,9,16,20,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,16,15)1
|1,3,4,7,8,2,5,9,16,20,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,7,8,2,5,9,16,20,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1
|1,3,4,7,8,2,5,9,16,20,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3
|1,3,4,7,8,2,5,9,16,20,13,20,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,15,11,8,5)3(22,*21,15,3,2,1,0)4(23,22,21,15)2(24,23,22)1(25,24,11,8,5)3
|1,3,4,7,8,2,5,9,16,20,13,20,24,17,24,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,16,15)1
|1,3,4,7,8,2,5,9,16,20,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,18,17,16,15)3(22,*21,18,17,16,15)3(23,21,18)1(24,23,11,8,5)3
|1,3,4,7,8,2,5,9,16,20,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,18,17)1
|1,3,4,7,8,2,5,9,16,20,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,20,19)1
|1,3,4,7,8,2,5,9,16,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,*20,19,3,2,1,0)4(22,21,20,19)2(23,22,21)1
|1,3,4,7,8,2,5,9,16,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,17,16,15)3
|1,3,4,7,8,2,5,9,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23)1(26,25,23,22,21)3
|1,3,4,7,8,2,5,9,16,21,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1
|1,3,4,7,8,2,5,9,16,21,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3(18,11,8,5)2(19,18,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,11,8,5)2(17,16,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,*19,18,3,2,1,0)4(21,20,19,18)2(22,21,20)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3(20,16,15,12)2(21,20,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34,27,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,12,11,8,5)3(18,*17,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,11,8,5)2(24,23,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32,37,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,*22,21,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,19,17,15)3
|1,3,4,7,8,2,5,9,16,21,15,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,18,17,15)2(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,23,36
|-
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|1,3,4,7,8,2,5,9,16,21,15,26,33,25
|-
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|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
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|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
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|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44,55,25,44
|-
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|1,3,4,7,8,2,5,9,16,21,16
|-
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|1,3,4,7,8,2,5,9,16,21,29
|-
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|1,3,4,7,8,2,5,9,16,22
|-
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|1,3,4,7,8,2,5,9,16,22,16
|-
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|1,3,4,7,8,2,5,9,16,22,29
|-
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|1,3,4,7,8,2,5,9,16,22,29,5
|-
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|1,3,4,7,8,2,5,9,16,22,29,16
|-
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|1,3,4,7,8,2,5,9,16,22,29,39
|-
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|1,3,4,7,8,2,5,9,16,22,30
|-
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|1,3,4,7,8,2,5,9,16,22,31,16
|-
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|1,3,4,7,8,2,5,9,16,22,33
|-
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|1,3,4,7,8,2,5,9,16,22,33,39
|-
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|1,3,4,7,8,2,5,9,16,22,33,43,33
|-
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|1,3,4,7,8,2,5,9,16,23
|-
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|1,3,4,7,8,2,5,9,16,23,30
|-
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|1,3,4,7,8,2,5,9,16,24
|-
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|1,3,4,7,8,3
|-
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|1,3,4,7,8,4,3
|-
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|1,3,4,7,8,6,11
|-
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|1,3,4,7,8,6,11,12,3
|-
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|1,3,4,7,8,7
|-
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|1,3,4,7,8,7,8,3
|-
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|1,3,4,7,8,8,3
|-
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|1,3,4,7,8,9
|-
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|1,3,4,7,8,9,2,5,9,16,24,28
|-
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|1,3,4,7,8,9,2,5,9,16,24,31
|-
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|1,3,4,7,8,9,2,5,9,16,24,32
|-
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|1,3,4,7,8,9,2,5,9,16,24,33
|-
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|1,3,4,7,8,9,3
|-
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|1,3,4,7,8,10
|-
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|1,3,4,7,8,11
|-
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|1,3,4,7,8,11,12,2,5,9,16,24,35,43
|-
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|1,3,4,7,8,11,12,3
|-
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|1,3,4,7,9
|-
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|1,3,4,7,9,6,11,15
|-
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|1,3,4,7,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,*17,14,12,11,8,5)4
|1,3,4,7,9,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5
|1,3,4,7,9,10,2,5,9,16,25,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,3,2,1,0)4(25,3,2)1
|1,3,4,7,9,10,2,5,9,16,25,32,40,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,12,11,8,5)4
|1,3,4,7,9,10,2,5,9,16,25,32,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2
|1,3,4,7,9,10,2,5,9,16,25,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,12,11)1
|1,3,4,7,9,10,2,5,9,16,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,22,21)1
|1,3,4,7,9,10,2,5,9,16,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,7,9,10,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,12,11,8,5)4
|1,3,4,7,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,20,17,14)3
|1,3,4,7,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1
|1,3,4,7,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,21,20)1
|1,3,4,7,9,14,18,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4
|1,3,4,7,9,14,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,24,23,22)2(26,25,24)1
|1,3,4,7,9,14,18,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4
|1,3,4,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5
|1,3,4,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,26,23)1
|1,3,4,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,3,2,1,0)4(30,3,2)1
|1,3,4,7,11,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,12,11)1
|1,3,4,7,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,29,26,23)2(31,30,29)1
|1,3,4,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,*11,*8,5,4,3,2,1,0)5
|1,3,5
|}
[[分类:分析]]

IBLP分析Part2

2026-04-30T16:30:30Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3
|1,2,4,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2
|1,2,4,8,10,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1
|1,2,4,8,10,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3
|1,2,4,8,10,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,9,8,7)2(14,13,9,8,7)3(15,*14,13,9,8,7)3
|1,2,4,8,10,6,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3
|1,2,4,8,10,6,10,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1
|1,2,4,8,10,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3
|1,2,4,8,10,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3(18,15,2,1,0)3
|1,2,4,8,10,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,2,1,0)3
|1,2,4,8,10,7,12,14,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,2,1,0)3(15,14,9)1(16,15,14,9)2(17,16,15,14,9)3(18,*17,16,15,14,9)3(19,16,2,1,0)3
|1,2,4,8,10,7,12,14,9,14,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2
|1,2,4,8,10,7,12,14,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,2,1,0)3
|1,2,4,8,10,7,12,14,10,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,2,1,0)3(21,15,14)1
|1,2,4,8,10,7,12,14,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3
|1,2,4,8,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3(17,9,8,7)2(18,17,9,8,7)3(19,*18,17,9,8,7)3
|1,2,4,8,10,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3(17,14,2,1,0)3
|1,2,4,8,10,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,10)1
|1,2,4,8,10,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,10,2,1,0)3
|1,2,4,8,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,2,1,0)3
|1,2,4,8,10,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,10)1
|1,2,4,8,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,10)1(15,14,13,10)2(16,15,14,13,10)3(17,*16,15,14,13,10)3
|1,2,4,8,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3
|1,2,4,8,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,8,7)1
|1,2,4,8,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3(18,15,14,8,7)3
|1,2,4,8,11,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2
|1,2,4,8,11,7,12,15,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1
|1,2,4,8,11,7,12,15,10,14
|-
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|-
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|-
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|1,2,4,8,13,12,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,4)1
|1,2,4,8,13,12,17,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,6,2,1,0)3(10,*9,6,3,2,1,0)4(11,9,6)1
|1,2,4,8,13,12,17,16,21,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,6,4)1
|1,2,4,8,13,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8)1
|1,2,4,8,13,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,2,1,0)3
|1,2,4,8,13,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,2,4,8,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,2,4,8,13,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2
|1,2,4,8,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3
|1,2,4,8,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,8,6,4)3
|1,2,4,8,13,18,23,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1
|1,2,4,8,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1(12,11,10,9)2(13,12,11,10,9)3
|1,2,4,8,13,19,25,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1(12,11,10,9)2(13,12,11,10,9)3(14,13,12)1
|1,2,4,8,13,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3
|1,2,4,8,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,9,8,6,4)3(13,*12,9,8,6,4)3
|1,2,4,8,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4
|1,2,4,8,13,20,27,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4(14,12,10)1
|1,2,4,8,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4
|1,2,4,8,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1
|1,2,4,8,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1(10,9,6,4)2(11,10,9,6,4)3(12,*11,10,9,6,4)3(13,11,9,6,4)3(14,*13,11,10,9,6,4)4(15,*13,11,10,9,6,4)4
|1,2,4,8,14,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,*6,4,3,2,1,0)4
|1,2,4,8,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7)1
|1,2,4,8,14,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,2,4,8,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4
|1,2,4,8,14,18,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9)1
|1,2,4,8,14,18,24,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,2,4,8,14,18,24,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2
|1,2,4,8,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,*6,4,3,2,1,0)4
|1,2,4,8,14,19,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,2,1,0)3(10,*9,7,3,2,1,0)4
|1,2,4,8,14,19,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,6,4)2
|1,2,4,8,14,19,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3
|1,2,4,8,14,19,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10)1
|1,2,4,8,14,19,23,29,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,19,23,29,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3
|1,2,4,8,14,19,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,7,6,4)3
|1,2,4,8,14,19,24,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1
|1,2,4,8,14,19,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,2,4,8,14,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*14,12,11,10,9,8)4
|1,2,4,8,14,19,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*6,4,3,2,1,0)4
|1,2,4,8,14,20,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2
|1,2,4,8,14,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3
|1,2,4,8,14,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4(13,8,7,6,4)(14,*13,8,3,2,1,0)4
|1,2,4,8,14,20,26,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,7,6,4)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,2,4,8,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4(12,*9,8,3,2,1,0)4
|1,2,4,8,14,22,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,7,6,4)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,12,11)1
|1,2,4,8,14,22,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,22,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,10,9,8)2(15,14,10,9,8)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,30,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,10,9,8)3(15,*14,13,3,2,1,0)4
|1,2,4,8,14,22,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,14,22,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3
|1,2,4,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3(14,12,2,1,0)3(15,*14,12,11,2,1,0)4(16,15,14,12)2(17,16,15,14,12)3(18,*17,16,15,14,12)3
|1,2,4,8,15,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,3,2,1,0)3(12,*11,3,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3
|1,2,4,8,15,12,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,6,4)1
|1,2,4,8,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4
|1,2,4,8,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4(12,11,6,4)2(13,12,11,6,4)3(14,*13,12,11,6,4)3
|1,2,4,8,15,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4
|1,2,4,8,15,14,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4(13,12,11,7)2(14,13,12,11,7)3(15,*14,13,12,11,7)3
|1,2,4,8,15,14,23,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2
|1,2,4,8,15,14,23,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,7,6,4)3(15,*14,12,3,2,1,0)4
|1,2,4,8,15,14,23,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,11)1
|1,2,4,8,15,14,23,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,7,6,4)3(15,*14,13,3,2,1,0)4
|1,2,4,8,15,14,23,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,15,14,23,20,28,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,2,4,8,15,14,23,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,12,11)1
|1,2,4,8,15,14,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4(18,17,12,11)2(19,18,17,12,11)3(20,*19,18,17,12,11)3
|1,2,4,8,15,14,23,22,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,13,12,11)2
|1,2,4,8,15,14,23,22,33,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,7,6,4)3
|1,2,4,8,15,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3
|1,2,4,8,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,17,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,2,1,0)3
|1,2,4,8,15,17,14,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,12,11,8)2(14,13,12,11,8)3(15,*14,13,12,11,8)3
|1,2,4,8,15,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3
|1,2,4,8,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,20,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3
|1,2,4,8,15,20,14,23,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3(19,14,13,12)2(20,19,14,13,12)3(21,*20,19,14,13,12)3
|1,2,4,8,15,20,14,23,28,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,14,13,12)3
|1,2,4,8,15,20,14,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,20,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,8,7,6,4)3
|1,2,4,8,15,20,20
|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|1,2,4,8,15,25,39,50
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|1,2,4,8,15,26
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|1,2,4,8,15,26,34
|-
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|-
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|-
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|1,2,4,8,16
|}
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|1,2,4,8,16,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3
|1,2,4,8,16,12,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4
|1,2,4,8,16,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,9,2,1,0)3(20,*19,9,3,2,1,0)4
|1,2,4,8,16,12,20,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,11,2,1,0)3(20,*19,11,3,2,1,0)4
|1,2,4,8,16,12,20,16,24,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,11,9)1
|1,2,4,8,16,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4
|1,2,4,8,16,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2
|1,2,4,8,16,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,3,2,1,0)4
|1,2,4,8,16,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3
|1,2,4,8,16,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3(23,21,19,11,9)3(24,*23,21,20,19,11,9)4(25,*24,*23,21,20,19,11,9)4
|1,2,4,8,16,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2
|1,2,4,8,16,14,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,3,2,1,0)4
|1,2,4,8,16,14,22,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3
|1,2,4,8,16,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3(22,20,12,11,9)3(23,*22,20,19,12,11,9)4(,24,*23,*22,20,19,12,11,9)4
|1,2,4,8,16,15,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3
|1,2,4,8,16,15,27,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3
|1,2,4,8,16,15,27,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3(21,19,12,11,9)3(22,*21,19,13,12,11,9)
4(23,22,21,19)2(24,23,22,21,19)3(25,*24,23,22,21,19)3(26,24,22,21,19)3(27,*26,24,23,22,21,19)4(28,*27,*26,24,23,22,21,19)4
|1,2,4,8,16,15,27,22,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,*12,*11,9,3,2,1,0)4
|1,2,4,8,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3
|1,2,4,8,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3
|1,2,4,8,16,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3(13,11,2,1,0)3(14,*13,11,10,2,1,0)4(15,*14,*13,11,10,2,1,0)4
|1,2,4,8,16,19,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,2,4,8,16,19,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4
|1,2,4,8,16,19,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,12,10)1
|1,2,4,8,16,19,12,20,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,*12,10,3,2,1,0)4
|1,2,4,8,16,19,12,20,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3
|1,2,4,8,16,19,12,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3(23,21,13,12,10)3(24,*23,21,20,13,12,10)4(25,*24,*23,21,20,13,12,10)4
|1,2,4,8,16,19,12,20,19,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,14,13,12,10)3(21,*20,14,13,12,10)3(22,20,13,12,10)3(23,*22,20,14,13,12,10)4(24,*23,*22,20,14,13,12,10)4
|1,2,4,8,16,19,12,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3
|1,2,4,8,16,19,12,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,2,1,0)2(22,21,2,1,0)3(23,*22,21,2,1,0)3
|1,2,4,8,16,19,12,20,23,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,14,13,12,10)3(22,*21,14,13,12,11,10)3(23,21,13,12,10)3(24,*23,21,14,13,12,10)4(25,*24,*23,21,14,13,12,10)4
|1,2,4,8,16,19,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4
|1,2,4,8,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,20,15)1
|1,2,4,8,16,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,21,20,15)
2(23,22,21,20,15)3(24,*23,22,21,20,15)3(25,23,21,20,15)3(26,*25,23,22,21,20,15)4(27,*26,*25,23,22,21,20,15)4
|1,2,4,8,16,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,13,12,10)3
|1,2,4,8,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,2,4,8,16,21,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,4,2,1,0)4
|1,2,4,8,16,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,2,1,0)4
|1,2,4,8,16,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,4)1
|1,2,4,8,16,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4
|1,2,4,8,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4
|1,2,4,8,16,22,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,2,1,0)3(22,*21,16,3,2,1,0)
4(23,22,21,16)2(24,23,22,21,16)3(25,*24,23,22,21,16)3(26,24,22,21,16)3(27,*26,24,23,22,21,16)4(28,*27,*26,24,23,22,21,16)4
|1,2,4,8,16,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,14,13,11)3(22,*21,16,15,14,13,11)4(23,15,14,13,11)3(24,*23,15,14,13,11)3(25,23,14,13,11)3(26,*25,23,15,14,13,11)4
|1,2,4,8,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,2,4,8,16,23,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,4,2,1,0)3
|1,2,4,8,16,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3
|1,2,4,8,16,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,16,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,4)1
|1,2,4,8,16,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*9,4,3,2,1,0)4
|1,2,4,8,16,23,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2
|1,2,4,8,16,23,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3
|1,2,4,8,16,23,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3(14,12,10,9,4)3(15,*14,12,11,10,9,4)4(16,*15,*14,12,11,10,9,4)4
|1,2,4,8,16,23,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*10,*9,4,3,2,1,0)4
|1,2,4,8,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,*13,*12,9,4,3,2,1,0)5
|1,2,4,8,16,24,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,6)1
|1,2,4,8,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4
|1,2,4,8,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,3,2,1,0)3(14,*13,3,2,1,0)3(15,13,2,1,0)3(16,*15,13,3,2,1,0)4(17,*16,*15,13,3,2,1,0)4
|1,2,4,8,16,27,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5(14,*9,6,3,2,1,0)4(15,*14,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2
|1,2,4,8,16,28,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4
|1,2,4,8,16,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,13,12)1
|1,2,4,8,16,28,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,*13,12,3,2,1,0)4(17,*16,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,14,13,12)2
|1,2,4,8,16,28,44,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,10,9,6)3
|1,2,4,8,16,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*10,*0,6,4,3,2,1,0)5
|1,2,4,8,16,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,2,1,0)3(13,*12,11,3,2,1,0)4(14,*13,*12,11,4,3,2,1,0)5
|1,2,4,8,16,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3
|1,2,4,8,16,30,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5
|1,2,4,8,16,30,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,14,12)1
|1,2,4,8,16,30,45
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,16,15,14,12)3
|1,2,4,8,16,30,52,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
|1,2,4,8,16,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
(17,14,10,9,6)3(18,*17,14,11,10,9,6)4(19,*18,*17,14,12,11,10,9,6)5(20,19,18,17,14)3(21,*20,19,18,17,14)3(22,20,18,17,16)3(23,*22,20,19,18,17,14)4(24,*23,*22,20,19,18,17,14)4
|1,2,4,8,16,31,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5(13,9,2,1,0)3(14,*13,9,3,2,1,0)4(15,*14,*13,9,4,3,2,1,0)5(16,*15,*14,*13,9,6,4,3,2,1,0)6(17,*16,*15,*14,*13,9,6,4,3,2,1,0)6
|1,2,4,8,16,32,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|}
[[分类:分析]]

IBLP分析Part3

2026-04-30T16:28:58Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1
|1,3,2,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1
|1,3,2,5,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1
|1,3,2,5,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2
|1,3,2,5,4,9,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1
|1,3,2,5,4,9,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,9,8)1
|1,3,2,5,4,9,6,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,*9,8,7,6,5)3
|1,3,2,5,4,9,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1
|1,3,2,5,4,9,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,2,1,0)3(11,10,6)1(12,11,10,6)2(13,12,11)1
|1,3,2,5,4,9,6,11,8,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1
|1,3,2,5,4,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1
|1,3,2,5,4,9,7,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2
|1,3,2,5,4,9,7,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1
|1,3,2,5,4,9,7,13,10,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1(15,11,10)1
|1,3,2,5,4,9,7,13,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3
|1,3,2,5,4,9,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3(8,6,2,1,0)3(9,*8,6,5,2,1,0)3(10,*9,*8,6,5,2,1,0)4
|1,3,2,5,4,9,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2)1
|1,3,2,5,4,9,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3
|1,3,2,5,4,9,8,17,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,2,5,4,9,8,17,11,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,2,1,0)3
|1,3,2,5,4,9,8,17,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1
|1,3,2,5,4,9,8,17,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6,5,3)3(9,*8,7,6,5,3)3
|1,3,2,5,4,9,8,17,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1
|1,3,2,5,4,9,8,17,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1
|1,3,2,5,4,9,8,17,11,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1(10,9,5,3)2(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2
|1,3,2,5,4,9,8,17,11,17,15,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,*10,9,6,5,3)3
|1,3,2,5,4,9,8,17,11,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,)1
|1,3,2,5,4,9,8,17,11,17,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3
|1,3,2,5,4,9,8,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,3,2,5,4,9,8,17,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1
|1,3,2,5,4,9,8,17,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1
|1,3,2,5,4,9,8,17,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1(15,14,9,8)2(16,15,14)1
|1,3,2,5,4,9,8,17,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3
|1,3,2,5,4,9,8,17,13,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4
|1,3,2,5,4,9,8,17,13,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1
|1,3,2,5,4,9,8,17,13,21,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1(17,16,14,11)2(18,17,16)1
|1,3,2,5,4,9,8,17,13,21,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2
|1,3,2,5,4,9,8,17,13,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2(15,14,11)1
|1,3,2,5,4,9,8,17,13,21,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,18,26,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1
|1,3,2,5,4,9,8,17,13,21,18,26,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1(18,14,12)1
|1,3,2,5,4,9,8,17,13,21,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,*14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,3,2,5,4,9,8,17,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2
|1,3,2,5,4,9,8,17,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1
|1,3,2,5,4,9,8,17,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3
|1,3,2,5,4,9,8,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3(13,11,8,7,5)3(14,*13,11,9,8,7,5)4(15,14,13,11,)2(16,15,14)1
|1,3,2,5,4,9,8,17,15,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3
|1,3,2,5,4,9,8,17,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,*11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,10,7)1
|1,3,2,5,4,9,8,17,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*10,7,3,2,1,0)4(14,*13,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1
|1,3,2,5,4,9,8,17,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,5,3,2,1,0)5(14,*13,*12,*11,8,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,33,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,5)1
|1,3,2,5,4,9,8,17,16,33,32,65
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1
|1,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1(6,3,2)1
|1,3,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1
|1,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1)1(7,6,1)1(8,7,6,1)2(9,8,7)1(10,9)1
|1,3,4,2,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1
|1,3,4,2,5,6,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8)1
|1,3,4,2,5,6,4,9,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,6,4,9,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2)1(8,7)1
|1,3,4,2,5,6,4,9,10,8,17,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2,1,0)2(7,*6,3,2,1,0)3(8,6,3)1(9,8)1
|1,3,4,2,5,6,4,9,10,8,17,18,16,33,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2)1
|1,3,4,2,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1
|1,3,4,2,5,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3
|1,3,4,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1)1(7,6,1,)2(8,7,6,1)2(9,8,7)1(10,9,8,6,1)3
|1,3,4,2,5,7,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1
|1,3,4,2,5,7,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8,6,1,0)3
|1,3,4,2,5,7,4,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2
|1,3,4,2,5,7,4,9,11,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1
|1,3,4,2,5,7,4,9,11,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3
|1,3,4,2,5,7,4,9,11,6,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1
|1,3,4,2,5,7,4,9,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1(13,12,7,6)2(14,13,12)1(15,14,2,1,0)3
|1,3,4,2,5,7,4,9,11,7,13,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8,7,6)3(13,*12,9,8,7,6)3
|1,3,4,2,5,7,4,9,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8)1
|1,3,4,2,5,7,4,9,11,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3
|1,3,4,2,5,7,4,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3(12,8,7,6)2(13,12,8,7,6)3(14,13,12)1(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3
|1,3,4,2,5,7,4,9,12,7,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,7,4,9,12,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3(9,7,2,1,0)3(10,*9,7,6,2,1,0)4(11,*10,*9,7,6,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,4,2,5,7,4,9,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1(8,7,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,20,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,2,1,0)3(9,*8,6,3,2,1,0)4(10,*9,*8,6,3,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,17,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1
|1,3,4,2,5,7,4,9,12,8,17,22,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,2,1,0)3(11,*10,6,3,2,1,0)4(12,*11,*10,6,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,*14,*13,10,6,3,2,1,0)5(16,*15,*14,*13,10,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,3)
|1,3,4,2,5,7,4,9,12,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,2,1,0)3
|1,3,4,2,5,7,4,9,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,4,9,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,4,9,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,4,9,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,3,4,2,5,7,4,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,2,1,0)2(12,11,2)1(13,12,2,1,0)3(14,11,2,1,0)3(15,*14,11,2,1,0)3(16,14,11)1(17,16,2,1,0)3(18,*17,16,11,2,1,0)4
|1,3,4,2,5,7,4,9,13,8,17,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1
|1,3,4,2,5,7,4,9,13,8,17,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,13,8,17,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1
|1,3,4,2,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,3,2)1
|1,3,4,2,5,7,5,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3
|1,3,4,2,5,7,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,4,2,1,0)3
|1,3,4,2,5,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,2,1,0)3
|1,3,4,2,5,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1
|1,3,4,2,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1
|1,3,4,2,5,7,10,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,8,7)1
|1,3,4,2,5,7,10,4,9,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,18,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,6,11,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,8,2,1,0)3(11,*10,8,7,2,1,0)4(12,*11,*10,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,18,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,14,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,2,1,0)3(17,*16,13,3,2,1,0)4(18,*17,*16,13,7,3,2,1,0)5(19,16,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,4,9,13,18,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,7,4)1
|1,3,4,2,5,7,10,4,9,13,18,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,5,4)1
|1,3,4,2,5,7,10,4,9,13,18,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2
|1,3,4,2,5,7,10,4,9,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,26,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,5,4)1(11,10,5,4)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,6,5,4)2(11,10,6)1(12,11,2,1,0)3(13,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,28,36,40,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,10,7)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,30,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43,47,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28,36,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,11,10,7)3
|1,3,4,2,5,7,10,4,9,13,18,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,32,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,10,4,9,13,18,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,*10,9,8,7,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,19,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3
|1,3,4,2,5,7,10,4,9,13,19,6,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,7,2,1,0)3(15,14,7)1(16,15,14,7)2(17,16,15)1(18,17,15,14,7)3(19,*18,17,16,15,14,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21,8,13,17,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,19,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1(15,14,8,7)2(16,15,14)1(17,16,14,8,7)3(18,*17,16,15,14,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,7,13,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,*9,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,14,13)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,2,1,0)3(17,*16,9,3,2,1,0)4(18,16,9)1(19,18,16,9)2(20,19,18)1(21,20,18,16,9)3(22,*21,20,19,18,16,9)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39,16,25,33,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1(19,18,16,9,7)3(20,*19,18,17,16,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,2,1,0)3(17,*16,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,37,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,9,7)2(17,16,11)1(18,17,11,9,7)3(19,*18,17,16,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23,31,38,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4(22,16,12)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32,43,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,10,9,7)2
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,15,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1(23,22,20,18,17)3(24,*23,22,21,20,18,17)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28,40,54
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4(15,11,10,9,7)3(16,*15,11,10,9,7)3(17,15,10,9,7)3(18,*17,15,11,10,9,7)4(19,18,17,15)2(20,19,18)1(21,20,18,17,15)3(22,*21,20,19,18,17,15)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,15,28,40,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,36,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,2,1,0)2(12,*11,7,3,2,1,0)3(13,*12,*11,7,3,2,1,0)4(14,11,7)1(15,14,2,1,0)3(16,11,2,1,0)3(17,*16,11,3,2,1,0)4(18,*17,*16,11,7,3,2,1,0)5(19,*18,*17,*16,11,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,53
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67,24,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,7,3,2,1,0)5(20,*17,16,3,2,1,0)4(21,*20,*17,16,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,12,11,10,9)3(17,*16,12,11,10,9)3(18,16,12)1(19,18,11,10,9)3(20,*19,18,12,11,10,9)4
|1,3,4,2,5,7,10,4,9,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,20,8,17,25,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1
|1,3,4,2,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,5,7,10,4,9,13,20,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,*7,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,5,4)1
|1,3,4,2,5,7,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,7,10,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,7,6)1
|1,3,4,2,5,7,10,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,*7,6,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,12,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2
|1,3,4,2,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,10,9,8)3(16,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,24,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,13,12)2
|1,3,4,2,5,7,10,13,4,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17,25,40,49,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,24,31,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,13,4,9,13,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2
|1,3,4,2,5,7,10,13,4,9,13,20,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1(15,14,12,11,10)3(16,*15,14,13,12,11,10)4
|1,3,4,2,5,7,10,13,4,9,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,7,10,13,4,9,13,20,27,8,17,25,40,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2)1
|1,3,4,2,5,7,10,13,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,4,2,1,0)3
|1,3,4,2,5,7,10,13,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,5,4)1
|1,3,4,2,5,7,10,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,*5,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,13,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,6,5,4)2
|1,3,4,2,5,7,10,13,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3
|1,3,4,2,5,7,10,13,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,2,1,0)2(10,9,2)1(11,10,2,1,0)3(12,*11,10,9,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3
|1,3,4,2,5,7,10,13,16,4,9,13,20,27,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,3,2)1
|1,3,4,2,5,7,10,13,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1
|1,3,4,2,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,15,14)1
|1,3,4,2,5,7,10,14,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,3,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,28,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,11,10,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2
|1,3,4,2,5,7,10,14,4,9,13,20,29,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,10,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*18,16,15,14,13,12)4(21,10,3)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,20,19,18,16)4(27,20,19,18,16)3(28,*27,20,19,18,16)3(29,27,20)1(30,29,19,18,16)3(31,*30,29,20,19,18,16)4(32,*31,*30,29,27,20,19,18,16)5(33,32,31,30,29)3(34,*33,32,31,30,29)3(35,33,31,30,29)3(36,*35,33,32,31,30,29)4
|1,3,4,2,5,7,10,14,4,9,13,20,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*19,*18,16,10,3,2,1,0)5
|1,3,4,2,5,7,10,14,4,9,13,20,31,8,17,25,40,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,3,2)1
|1,3,4,2,5,7,10,14,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,*10,9,3,2,1,0)4(12,3,2)1
|1,3,4,2,5,7,10,14,17,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2
|1,3,4,2,5,7,10,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,3,2)1
|1,3,4,2,5,7,10,14,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3
|1,3,4,2,5,7,10,14,18,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,11,10)1
|1,3,4,2,5,7,10,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,10,14,19,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3
|1,3,4,2,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,11,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,2,5,7,11,4,9,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,11,4,9,13,21,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1
|1,3,4,2,5,7,11,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,4,2,1,0)3(11,*10,4,3,2,1,0)4(12,11,10,4)2(13,12,11,10,4)3(14,*13,12,11,10,4)3
|1,3,4,2,5,7,11,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,11,10,5)2(13,12,11,10,5)3(14,*13,12,11,10,5)3
|1,3,4,2,5,7,11,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,4)1
|1,3,4,2,5,7,11,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,11,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,10,5,4)2(12,11,10,5,4)3(13,*12,11,10,5,4)3
|1,3,4,2,5,7,11,10,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2
|1,3,4,2,5,7,11,10,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,10,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3(16,12,11,10)2
|1,3,4,2,5,7,11,10,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,6,5,4)3
|1,3,4,2,5,7,11,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3
|1,3,4,2,5,7,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,11,10,7)2(13,12,11,10,7)3(14,*13,12,11,10,7)3
|1,3,4,2,5,7,11,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3
|1,3,4,2,5,7,11,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,10,8)1
|1,3,4,2,5,7,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,11,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,11,10,8)2(13,12,11,10,8)3(14,*13,12,11,10,8)3(15,13,11,10,8)3(16,*15,13,12,11,10,8)4
|1,3,4,2,5,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*11,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,7,6)1
|1,3,4,2,5,7,12,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,12,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,2,1,0)3
|1,3,4,2,5,7,12,14,11,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,12,14,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,12,16,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,9,8)1
|1,3,4,2,5,7,12,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,12,16,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4
|1,3,4,2,5,7,12,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,12,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*15,*14,12,11,10,9,8)4
|1,3,4,2,5,7,12,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,11,10)1
|1,3,4,2,5,7,12,16,25,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,2,5,7,12,16,25,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4
|1,3,4,2,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,1,0)1(9,8,1,0)2(10,9,8)1(11,10,8,1,0)3(12,*11,10,9,8,1,0)4(13,*12,*11,10,9,8,1,0)4
|1,3,4,2,5,8,4,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,8,4,9,14,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4
|1,3,4,2,5,8,4,9,14,6,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1
|1,3,4,2,5,8,4,9,14,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1(17,16,9,8)2(18,17,16)1(1918,16,9,8)3(20,*19,18,17,16,9,8)4(21,*20,*19,*18,17,16,9,8)4
|1,3,4,2,5,8,4,9,14,7,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,8,4,9,14,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,8,4,9,14,8,17
|-
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|1,3,4,2,5,8,4,9,14,8,17,26
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,33
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,72
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,50
|-
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|1,3,4,2,5,8,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*10,*9,8,3,2,1,0)4
|1,3,4,2,5,8,5,8
|-
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|1,3,4,2,5,8,7
|-
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|1,3,4,2,5,8,7,5
|-
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|1,3,4,2,5,8,7,5,7,12
|-
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|1,3,4,2,5,8,7,5,7,12,17
|-
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|1,3,4,2,5,8,7,5,7,12,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,3,2,1,0)4
|1,3,4,2,5,8,7,5,8
|-
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|1,3,4,2,5,8,7,10
|-
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|1,3,4,2,5,8,7,10,5
|-
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|1,3,4,2,5,8,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1
|1,3,4,2,5,8,7,12
|-
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|1,3,4,2,5,8,7,12,17
|-
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|1,3,4,2,5,8,7,12,17,11
|-
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|1,3,4,2,5,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3
|1,3,4,2,5,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(6,3,2)1
|1,3,4,2,5,8,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5
|1,3,4,2,5,8,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,4,3,2,1,0)5
|1,3,4,2,5,8,11,14
|-
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|1,3,4,2,5,9
|-
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|1,3,4,2,5,9,4,9,14
|-
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|1,3,4,2,5,9,4,9,14,19
|-
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|1,3,4,2,5,9,4,9,15
|-
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|1,3,4,2,5,9,4,9,15,8,17
|-
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|1,3,4,2,5,9,4,9,15,9
|-
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|1,3,4,2,5,9,4,9,16
|-
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|1,3,4,2,5,9,4,9,16,8,17
|-
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|1,3,4,2,5,9,4,9,16,8,17,26
|-
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|1,3,4,2,5,9,4,9,16,8,17,27
|-
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|1,3,4,2,5,9,4,9,16,8,17,28
|-
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|1,3,4,2,5,9,4,9,16,8,17,28,12
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50,67
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,51
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,12,3)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,55,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*10,15,3,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*10,15,3,2,1,0)4(25,12,3)1
|1,3,4,2,5,9,4,9,16,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*23,*19,15,12,3,2,1,0)5
|1,3,4,2,5,9,4,9,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|}
[[分类:分析]]

iBLP

2026-04-29T14:49:51Z

Baixie01000a7：/* 分析 */

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达ω-Y(1,4)，对应(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2。
{| class="wikitable"
|+
!ω-Y序列
!iBLP
|-
|1,2
|(1,0)1(2,1)1
|-
|1,2,4
|(1,0)1(2,1,0)1
|-
|1,2,4,8
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3
|-
|1,2,4,8,16
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4
|-
|1,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|-
|1,3,4,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|-
|1,3,7
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*9,*8,5,4,3,2,1,0)5
|-
|1,3,9
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*10,*9,*8,5,4,3,2,1,0)5
|-
|1,3,10
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,4)1
|-
|1,4
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2
|}

{{默认排序:序数记号}}
[[分类:记号]]

iBLP

2026-04-26T09:44:19Z

Baixie01000a7：

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达1-Y(1,3,8)，对应(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,10,9)1。

{{默认排序:序数记号}}
[[分类:记号]]

IBLP分析Part4

2026-04-25T14:37:16Z

Baixie01000a7：创建页面，内容为“{| class="wikitable" |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1 |1,3,4,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1 |1,3,4,3,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,…”

{| class="wikitable"
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1
|1,3,4,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1
|1,3,4,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1
|1,3,4,3,4,2,5,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1(27,26)1
|1,3,4,3,4,2,5,9,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2)1
|1,3,4,3,4,2,5,9,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3
|1,3,4,3,4,2,5,9,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,3,4,2,5,9,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,2,1,0)3(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,12)1
|1,3,4,3,4,2,5,9,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2
|1,3,4,3,4,2,5,9,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,3,4,2,5,9,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,3,4,2,5,9,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,3,4,2,5,9,5,7,12
|-
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|1,3,4,3,4,2,5,9,5,7,12,16,25
|-
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|1,3,4,3,4,2,5,9,5,7,12,17
|-
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|1,3,4,3,4,2,5,9,5,7,12,17,22
|-
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|1,3,4,3,4,2,5,9,5,7,12,18
|-
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|1,3,4,3,4,2,5,9,5,7,12,18,5
|-
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|1,3,4,3,4,2,5,9,5,7,12,19
|-
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|1,3,4,3,4,2,5,9,5,7,12,21,12
|-
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|1,3,4,3,4,2,5,9,5,8
|-
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|1,3,4,3,4,2,5,9,5,8,11
|-
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|1,3,4,3,4,2,5,9,5,9
|-
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|1,3,4,3,4,2,5,9,5,9,4,9,18,9,16
|-
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|1,3,4,3,4,3
|-
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|1,3,4,4
|-
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|1,3,4,4,2,5,9,5
|-
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|1,3,4,4,2,5,9,6
|-
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|1,3,4,4,2,5,9,6,5
|-
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|1,3,4,4,2,5,9,7
|-
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|1,3,4,4,2,5,9,7,10,5
|-
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|1,3,4,4,2,5,9,7,11
|-
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|1,3,4,4,2,5,9,7,12
|-
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|1,3,4,4,2,5,9,8
|-
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|1,3,4,4,2,5,9,8,11
|-
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|1,3,4,4,2,5,9,8,12
|-
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|1,3,4,4,2,5,9,8,12,4,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,19
|-
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|-
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|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,26
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,29
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,21
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,23
|-
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|1,3,4,4,2,5,9,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,8
|-
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|1,3,4,4,2,5,9,8,12,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,9
|-
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|1,3,4,4,2,5,9,8,12,10
|-
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|1,3,4,4,2,5,9,8,12,11
|-
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|1,3,4,4,2,5,9,8,12,11,15
|-
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|1,3,4,4,2,5,9,8,12,11,15,5
|-
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|1,3,4,4,2,5,9,8,12,11,15,12
|-
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|1,3,4,4,2,5,9,8,12,11,15,14,18
|-
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|1,3,4,4,2,5,9,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,15
|-
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|1,3,4,4,2,5,9,9,4,9,18,15,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,16
|-
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|1,3,4,4,2,5,9,9,4,9,18,18
|-
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|1,3,4,4,3
|-
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|1,3,4,4,3,4,4,3
|-
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|1,3,4,4,4
|-
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|1,3,4,4,4,2,5,9,9,6,5
|-
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|1,3,4,4,4,2,5,9,9,9
|-
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|1,3,4,4,4,2,5,9,9,9,4,9,18,18,16
|-
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|1,3,4,4,4,3
|-
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|1,3,4,5
|-
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|1,3,4,5,2,5,9,10
|-
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|1,3,4,5,2,5,9,10,5
|-
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|1,3,4,5,2,5,9,10,7
|-
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|1,3,4,5,2,5,9,10,8
|-
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|1,3,4,5,2,5,9,10,8,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,13
|-
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|1,3,4,5,2,5,9,10,8,12,13,11,15,16,14,18,19
|-
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|1,3,4,5,2,5,9,10,9
|-
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|1,3,4,5,2,5,9,10,9,5
|-
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|1,3,4,5,2,5,9,10,10
|-
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|1,3,4,5,2,5,9,10,13
|-
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|1,3,4,5,2,5,9,11
|-
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|1,3,4,5,2,5,9,11,16
|-
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|1,3,4,5,2,5,9,11,16,22
|-
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|1,3,4,5,2,5,9,11,16,25,16
|-
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|1,3,4,5,2,5,9,11,16,25,27
|-
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|1,3,4,5,2,5,9,11,16,25,29
|-
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|1,3,4,5,2,5,9,12
|-
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|1,3,4,5,2,5,9,12,15
|-
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|1,3,4,5,2,5,9,12,16
|-
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|1,3,4,5,2,5,9,12,16,5
|-
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|1,3,4,5,2,5,9,12,16,16
|-
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|1,3,4,5,2,5,9,12,16,16,5
|-
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|1,3,4,5,2,5,9,12,16,19
|-
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|1,3,4,5,2,5,9,12,16,19,23,5
|-
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|1,3,4,5,2,5,9,13
|-
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|1,3,4,5,2,5,9,13,17
|-
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|1,3,4,5,2,5,9,14
|-
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|1,3,4,5,2,5,9,14,4,9,18,28
|-
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|1,3,4,5,2,5,9,14,4,9,18,28,9
|-
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|1,3,4,5,2,5,9,14,4,9,18,29
|-
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|1,3,4,5,3
|-
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|1,3,4,5,4
|-
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|1,3,4,5,4,2,5,9,14,6,5
|-
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|1,3,4,5,4,2,5,9,14,9
|-
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|1,3,4,5,4,2,5,9,14,9,4,9,18,32,16
|-
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|1,3,4,5,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15)1
|1,3,4,5,4,5
|-
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|1,3,4,5,4,5,2,5,9,14,9,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2
|1,3,4,5,4,5,2,5,9,14,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,17,16)1
|1,3,4,5,4,5,2,5,9,14,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,3,2,1,0)4
|1,3,4,5,4,5,2,5,9,14,9,14,4,9,18,32,18,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,3,2,1,0)4(19,3,2)1
|1,3,4,5,4,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11)1
|1,3,4,5,5
|-
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|1,3,4,5,5,2,5,9,14,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,2,1,0)3
|1,3,4,5,5,2,5,9,14,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2
|1,3,4,5,5,2,5,9,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2(16,15,11,8,5)2(17,16,15)1
|1,3,4,5,5,2,5,9,14,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3
|1,3,4,5,5,2,5,9,14,13,18,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,13,11,8,5)3(16,*15,13,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,21,26,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,13,12)1
|1,3,4,5,5,2,5,9,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*13,12,3,2,1,0)4(16,3,2)1
|1,3,4,5,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14)1
|1,3,4,5,6
|-
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|1,3,4,5,6,2,5,9,14,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,2,1,0)3
|1,3,4,5,6,2,5,9,14,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,4,3,2,1,0)5
|1,3,4,5,6,2,5,9,14,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,11,8,5)3
|1,3,4,5,6,2,5,9,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2
|1,3,4,5,6,2,5,9,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,5,6,2,5,9,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,5,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3
|1,3,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,3,2)1
|1,3,4,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,3,2)1
|1,3,4,6,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,15,8,5)3
|1,3,4,6,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1
|1,3,4,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1(16,3,2)1
|1,3,4,6,5,2,5,9,15,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2
|1,3,4,6,5,2,5,9,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,16,15)1
|1,3,4,6,5,2,5,9,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,*16,15,3,2,1,0)4(19,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2
|1,3,4,6,5,2,5,9,15,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3
|1,3,4,6,5,2,5,9,15,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2
|1,3,4,6,5,2,5,9,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,6,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,23,22,21)3
|1,3,4,6,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,6,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1
|1,3,4,6,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1(16,3,2)1
|1,3,4,6,7,2,5,9,15,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3
|1,3,4,6,7,2,5,9,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3(16,*15,12,3,2,1,0)4(17,*16,*15,12,4,3,2,1,0)5
|1,3,4,6,7,2,5,9,15,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,15,13)1
|1,3,4,6,7,2,5,9,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,3,2)1
|1,3,4,6,7,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,3,2,1,0)4(21,3,2)1
|1,3,4,6,7,8,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,17,15,13)3
|1,3,4,6,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,12,11,8,5)4
|1,3,4,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,16,15,13)2(18,17,16,15,13)3(19,*18,17,16,15,13)3
|1,3,4,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*16,*15,13,12,11,8,5)4
|1,3,4,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1
|1,3,4,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,12,11)1
|1,3,4,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1
|1,3,4,7,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2,1,0)3(16,*15,3,2,1,0)3(17,15,3)1(18,17,2,1,0)3(19,*18,17,3,2,1,0)4(20,*19,*18,17,15,3,2,1,0)5(21,*20,*19,*18,17,15,3,2,1,0)5(22,18,2,1,0)3(23,*22,18,3,2,1,0)4(24,*23,*22,18,15,3,2,1,0)5(25,*24,*23,*22,18,17,15,3,2,1,0)6(26,*23,*22,18,15,3,2,1,0)5(27,26,23,22,18)3(28,*27,26,23,22,18)3(29,27,26)1(30,29)1
|1,3,4,7,8,2,5,9,16,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2)1
|1,3,4,7,8,2,5,9,16,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,7,8,2,5,9,16,18
|-
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|1,3,4,7,8,2,5,9,16,19
|-
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|1,3,4,7,8,2,5,9,16,20
|-
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|1,3,4,7,8,2,5,9,16,20,4,9
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,39
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,8,17,35,69,79
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,9
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,41
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42,54,73
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,43
|-
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|1,3,4,7,8,2,5,9,16,20,5
|-
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|1,3,4,7,8,2,5,9,16,20,9
|-
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|1,3,4,7,8,2,5,9,16,20,9,4,9,18,34,43,16
|-
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|1,3,4,7,8,2,5,9,16,20,9,5
|-
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|1,3,4,7,8,2,5,9,16,20,9,16,20
|-
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|1,3,4,7,8,2,5,9,16,20,12
|-
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|1,3,4,7,8,2,5,9,16,20,13
|-
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|1,3,4,7,8,2,5,9,16,20,13,18
|-
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|1,3,4,7,8,2,5,9,16,20,13,18,5
|-
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|1,3,4,7,8,2,5,9,16,20,13,20
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24,17,24,28
|-
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|1,3,4,7,8,2,5,9,16,20,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,18,17,16,15)3(22,*21,18,17,16,15)3(23,21,18)1(24,23,11,8,5)3
|1,3,4,7,8,2,5,9,16,20,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,18,17)1
|1,3,4,7,8,2,5,9,16,20,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,20,19)1
|1,3,4,7,8,2,5,9,16,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,11,8,5)3(21,*20,19,3,2,1,0)4(22,21,20,19)2(23,22,21)1
|1,3,4,7,8,2,5,9,16,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,17,16,15)3
|1,3,4,7,8,2,5,9,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23)1(26,25,23,22,21)3
|1,3,4,7,8,2,5,9,16,21,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1
|1,3,4,7,8,2,5,9,16,21,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3(18,11,8,5)2(19,18,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,11,8,5)2(17,16,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,*19,18,3,2,1,0)4(21,20,19,18)2(22,21,20)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3(20,16,15,12)2(21,20,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34,27,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,12,11,8,5)3(18,*17,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,11,8,5)2(24,23,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32,37,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,*22,21,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,19,17,15)3
|1,3,4,7,8,2,5,9,16,21,15,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,18,17,15)2(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,23,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*18,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,15,11,8,5)3(20,*19,15,12,11,8,5)4(21,*20,*19,15,12,11,8,5)4(22,19,15)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44,55,25,44
|-
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|1,3,4,7,8,2,5,9,16,21,16
|-
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|1,3,4,7,8,2,5,9,16,21,29
|-
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|1,3,4,7,8,2,5,9,16,22
|-
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|1,3,4,7,8,2,5,9,16,22,16
|-
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|1,3,4,7,8,2,5,9,16,22,29
|-
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|1,3,4,7,8,2,5,9,16,22,29,5
|-
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|1,3,4,7,8,2,5,9,16,22,29,16
|-
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|1,3,4,7,8,2,5,9,16,22,29,39
|-
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|1,3,4,7,8,2,5,9,16,22,30
|-
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|1,3,4,7,8,2,5,9,16,22,31,16
|-
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|1,3,4,7,8,2,5,9,16,22,33
|-
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|1,3,4,7,8,2,5,9,16,22,33,39
|-
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|1,3,4,7,8,2,5,9,16,22,33,43,33
|-
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|1,3,4,7,8,2,5,9,16,23
|-
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|1,3,4,7,8,2,5,9,16,23,30
|-
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|1,3,4,7,8,2,5,9,16,24
|-
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|1,3,4,7,8,3
|-
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|1,3,4,7,8,4,3
|-
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|1,3,4,7,8,6,11
|-
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|1,3,4,7,8,6,11,12,3
|-
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|1,3,4,7,8,7
|-
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|1,3,4,7,8,7,8,3
|-
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|1,3,4,7,8,8,3
|-
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|1,3,4,7,8,9
|-
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|1,3,4,7,8,9,2,5,9,16,24,28
|-
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|1,3,4,7,8,9,2,5,9,16,24,31
|-
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|1,3,4,7,8,9,2,5,9,16,24,32
|-
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|1,3,4,7,8,9,2,5,9,16,24,33
|-
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|1,3,4,7,8,9,3
|-
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|1,3,4,7,8,10
|-
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|1,3,4,7,8,11
|-
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|1,3,4,7,8,11,12,2,5,9,16,24,35,43
|-
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|1,3,4,7,8,11,12,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4
|1,3,4,7,9
|-
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|1,3,4,7,9,6,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,12,11)1
|1,3,4,7,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,*17,14,12,11,8,5)4
|1,3,4,7,9,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5
|1,3,4,7,9,10,2,5,9,16,25,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,3,2,1,0)4(25,3,2)1
|1,3,4,7,9,10,2,5,9,16,25,32,40,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,12,11,8,5)4
|1,3,4,7,9,10,2,5,9,16,25,32,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2
|1,3,4,7,9,10,2,5,9,16,25,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,12,11)1
|1,3,4,7,9,10,2,5,9,16,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,22,21)1
|1,3,4,7,9,10,2,5,9,16,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,7,9,10,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,12,11,8,5)4
|1,3,4,7,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,20,17,14)3
|1,3,4,7,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1
|1,3,4,7,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,21,20)1
|1,3,4,7,9,14,18,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4
|1,3,4,7,9,14,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,24,23,22)2(26,25,24)1
|1,3,4,7,9,14,18,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4
|1,3,4,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5
|1,3,4,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,26,23)1
|1,3,4,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,3,2,1,0)4(30,3,2)1
|1,3,4,7,11,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,12,11)1
|1,3,4,7,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,29,26,23)2(31,30,29)1
|1,3,4,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,*11,*8,5,4,3,2,1,0)5
|1,3,5
|}

IBLP分析Part3

2026-04-25T14:36:45Z

Baixie01000a7：创建页面，内容为“{| class="wikitable" |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1 |1,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1 |1,3,2,5 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1 |1,3,2,5,4 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1 |1,3,2,5,4,9 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2 |1,3,2,5,4,9,6 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1 |1,3,2,5,4,9,6,9 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,…”

{| class="wikitable"
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1
|1,3,2,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1
|1,3,2,5,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1
|1,3,2,5,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2
|1,3,2,5,4,9,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1
|1,3,2,5,4,9,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,9,8)1
|1,3,2,5,4,9,6,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,*9,8,7,6,5)3
|1,3,2,5,4,9,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1
|1,3,2,5,4,9,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,2,1,0)3(11,10,6)1(12,11,10,6)2(13,12,11)1
|1,3,2,5,4,9,6,11,8,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1
|1,3,2,5,4,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1
|1,3,2,5,4,9,7,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2
|1,3,2,5,4,9,7,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1
|1,3,2,5,4,9,7,13,10,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1(15,11,10)1
|1,3,2,5,4,9,7,13,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3
|1,3,2,5,4,9,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3(8,6,2,1,0)3(9,*8,6,5,2,1,0)3(10,*9,*8,6,5,2,1,0)4
|1,3,2,5,4,9,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2)1
|1,3,2,5,4,9,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3
|1,3,2,5,4,9,8,17,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,2,5,4,9,8,17,11,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,2,1,0)3
|1,3,2,5,4,9,8,17,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1
|1,3,2,5,4,9,8,17,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6,5,3)3(9,*8,7,6,5,3)3
|1,3,2,5,4,9,8,17,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1
|1,3,2,5,4,9,8,17,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1
|1,3,2,5,4,9,8,17,11,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1(10,9,5,3)2(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2
|1,3,2,5,4,9,8,17,11,17,15,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,*10,9,6,5,3)3
|1,3,2,5,4,9,8,17,11,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,)1
|1,3,2,5,4,9,8,17,11,17,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3
|1,3,2,5,4,9,8,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,3,2,5,4,9,8,17,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1
|1,3,2,5,4,9,8,17,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1
|1,3,2,5,4,9,8,17,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1(15,14,9,8)2(16,15,14)1
|1,3,2,5,4,9,8,17,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3
|1,3,2,5,4,9,8,17,13,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4
|1,3,2,5,4,9,8,17,13,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1
|1,3,2,5,4,9,8,17,13,21,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1(17,16,14,11)2(18,17,16)1
|1,3,2,5,4,9,8,17,13,21,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2
|1,3,2,5,4,9,8,17,13,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2(15,14,11)1
|1,3,2,5,4,9,8,17,13,21,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,18,26,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1
|1,3,2,5,4,9,8,17,13,21,18,26,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1(18,14,12)1
|1,3,2,5,4,9,8,17,13,21,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,*14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,3,2,5,4,9,8,17,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2
|1,3,2,5,4,9,8,17,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1
|1,3,2,5,4,9,8,17,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3
|1,3,2,5,4,9,8,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3(13,11,8,7,5)3(14,*13,11,9,8,7,5)4(15,14,13,11,)2(16,15,14)1
|1,3,2,5,4,9,8,17,15,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3
|1,3,2,5,4,9,8,17,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,*11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,10,7)1
|1,3,2,5,4,9,8,17,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*10,7,3,2,1,0)4(14,*13,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1
|1,3,2,5,4,9,8,17,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,5,3,2,1,0)5(14,*13,*12,*11,8,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,33,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,5)1
|1,3,2,5,4,9,8,17,16,33,32,65
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1
|1,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1(6,3,2)1
|1,3,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1
|1,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1)1(7,6,1)1(8,7,6,1)2(9,8,7)1(10,9)1
|1,3,4,2,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1
|1,3,4,2,5,6,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8)1
|1,3,4,2,5,6,4,9,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,6,4,9,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2)1(8,7)1
|1,3,4,2,5,6,4,9,10,8,17,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2,1,0)2(7,*6,3,2,1,0)3(8,6,3)1(9,8)1
|1,3,4,2,5,6,4,9,10,8,17,18,16,33,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2)1
|1,3,4,2,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1
|1,3,4,2,5,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3
|1,3,4,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1)1(7,6,1,)2(8,7,6,1)2(9,8,7)1(10,9,8,6,1)3
|1,3,4,2,5,7,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1
|1,3,4,2,5,7,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8,6,1,0)3
|1,3,4,2,5,7,4,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2
|1,3,4,2,5,7,4,9,11,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1
|1,3,4,2,5,7,4,9,11,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3
|1,3,4,2,5,7,4,9,11,6,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1
|1,3,4,2,5,7,4,9,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1(13,12,7,6)2(14,13,12)1(15,14,2,1,0)3
|1,3,4,2,5,7,4,9,11,7,13,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8,7,6)3(13,*12,9,8,7,6)3
|1,3,4,2,5,7,4,9,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8)1
|1,3,4,2,5,7,4,9,11,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3
|1,3,4,2,5,7,4,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3(12,8,7,6)2(13,12,8,7,6)3(14,13,12)1(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3
|1,3,4,2,5,7,4,9,12,7,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,7,4,9,12,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3(9,7,2,1,0)3(10,*9,7,6,2,1,0)4(11,*10,*9,7,6,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,4,2,5,7,4,9,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1(8,7,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,20,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,2,1,0)3(9,*8,6,3,2,1,0)4(10,*9,*8,6,3,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,17,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1
|1,3,4,2,5,7,4,9,12,8,17,22,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,2,1,0)3(11,*10,6,3,2,1,0)4(12,*11,*10,6,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,*14,*13,10,6,3,2,1,0)5(16,*15,*14,*13,10,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,3)
|1,3,4,2,5,7,4,9,12,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,2,1,0)3
|1,3,4,2,5,7,4,9,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,4,9,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,4,9,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,4,9,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,3,4,2,5,7,4,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,2,1,0)2(12,11,2)1(13,12,2,1,0)3(14,11,2,1,0)3(15,*14,11,2,1,0)3(16,14,11)1(17,16,2,1,0)3(18,*17,16,11,2,1,0)4
|1,3,4,2,5,7,4,9,13,8,17,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1
|1,3,4,2,5,7,4,9,13,8,17,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,13,8,17,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1
|1,3,4,2,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,3,2)1
|1,3,4,2,5,7,5,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3
|1,3,4,2,5,7,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,4,2,1,0)3
|1,3,4,2,5,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,2,1,0)3
|1,3,4,2,5,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1
|1,3,4,2,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1
|1,3,4,2,5,7,10,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,8,7)1
|1,3,4,2,5,7,10,4,9,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,18,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,6,11,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,8,2,1,0)3(11,*10,8,7,2,1,0)4(12,*11,*10,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,18,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,14,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,2,1,0)3(17,*16,13,3,2,1,0)4(18,*17,*16,13,7,3,2,1,0)5(19,16,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,4,9,13,18,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,7,4)1
|1,3,4,2,5,7,10,4,9,13,18,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,5,4)1
|1,3,4,2,5,7,10,4,9,13,18,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2
|1,3,4,2,5,7,10,4,9,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,26,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,5,4)1(11,10,5,4)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,6,5,4)2(11,10,6)1(12,11,2,1,0)3(13,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,28,36,40,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,10,7)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,30,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43,47,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28,36,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,11,10,7)3
|1,3,4,2,5,7,10,4,9,13,18,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,32,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,10,4,9,13,18,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,*10,9,8,7,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,19,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3
|1,3,4,2,5,7,10,4,9,13,19,6,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,7,2,1,0)3(15,14,7)1(16,15,14,7)2(17,16,15)1(18,17,15,14,7)3(19,*18,17,16,15,14,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21,8,13,17,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,19,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1(15,14,8,7)2(16,15,14)1(17,16,14,8,7)3(18,*17,16,15,14,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,7,13,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,*9,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,14,13)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,2,1,0)3(17,*16,9,3,2,1,0)4(18,16,9)1(19,18,16,9)2(20,19,18)1(21,20,18,16,9)3(22,*21,20,19,18,16,9)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39,16,25,33,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1(19,18,16,9,7)3(20,*19,18,17,16,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,2,1,0)3(17,*16,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,37,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,9,7)2(17,16,11)1(18,17,11,9,7)3(19,*18,17,16,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23,31,38,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4(22,16,12)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32,43,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,10,9,7)2
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,15,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1(23,22,20,18,17)3(24,*23,22,21,20,18,17)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28,40,54
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4(15,11,10,9,7)3(16,*15,11,10,9,7)3(17,15,10,9,7)3(18,*17,15,11,10,9,7)4(19,18,17,15)2(20,19,18)1(21,20,18,17,15)3(22,*21,20,19,18,17,15)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,15,28,40,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,36,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,2,1,0)2(12,*11,7,3,2,1,0)3(13,*12,*11,7,3,2,1,0)4(14,11,7)1(15,14,2,1,0)3(16,11,2,1,0)3(17,*16,11,3,2,1,0)4(18,*17,*16,11,7,3,2,1,0)5(19,*18,*17,*16,11,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,53
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67,24,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,7,3,2,1,0)5(20,*17,16,3,2,1,0)4(21,*20,*17,16,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,12,11,10,9)3(17,*16,12,11,10,9)3(18,16,12)1(19,18,11,10,9)3(20,*19,18,12,11,10,9)4
|1,3,4,2,5,7,10,4,9,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,20,8,17,25,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1
|1,3,4,2,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,5,7,10,4,9,13,20,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,*7,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,5,4)1
|1,3,4,2,5,7,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,7,10,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,7,6)1
|1,3,4,2,5,7,10,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,*7,6,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,12,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2
|1,3,4,2,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,10,9,8)3(16,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,24,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,13,12)2
|1,3,4,2,5,7,10,13,4,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17,25,40,49,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,24,31,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,13,4,9,13,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2
|1,3,4,2,5,7,10,13,4,9,13,20,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1(15,14,12,11,10)3(16,*15,14,13,12,11,10)4
|1,3,4,2,5,7,10,13,4,9,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,7,10,13,4,9,13,20,27,8,17,25,40,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2)1
|1,3,4,2,5,7,10,13,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,4,2,1,0)3
|1,3,4,2,5,7,10,13,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,5,4)1
|1,3,4,2,5,7,10,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,*5,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,13,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,6,5,4)2
|1,3,4,2,5,7,10,13,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3
|1,3,4,2,5,7,10,13,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,2,1,0)2(10,9,2)1(11,10,2,1,0)3(12,*11,10,9,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3
|1,3,4,2,5,7,10,13,16,4,9,13,20,27,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,3,2)1
|1,3,4,2,5,7,10,13,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1
|1,3,4,2,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,15,14)1
|1,3,4,2,5,7,10,14,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,3,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,28,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,11,10,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2
|1,3,4,2,5,7,10,14,4,9,13,20,29,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,10,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*18,16,15,14,13,12)4(21,10,3)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,20,19,18,16)4(27,20,19,18,16)3(28,*27,20,19,18,16)3(29,27,20)1(30,29,19,18,16)3(31,*30,29,20,19,18,16)4(32,*31,*30,29,27,20,19,18,16)5(33,32,31,30,29)3(34,*33,32,31,30,29)3(35,33,31,30,29)3(36,*35,33,32,31,30,29)4
|1,3,4,2,5,7,10,14,4,9,13,20,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*19,*18,16,10,3,2,1,0)5
|1,3,4,2,5,7,10,14,4,9,13,20,31,8,17,25,40,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,3,2)1
|1,3,4,2,5,7,10,14,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,*10,9,3,2,1,0)4(12,3,2)1
|1,3,4,2,5,7,10,14,17,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2
|1,3,4,2,5,7,10,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,3,2)1
|1,3,4,2,5,7,10,14,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3
|1,3,4,2,5,7,10,14,18,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,11,10)1
|1,3,4,2,5,7,10,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,10,14,19,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3
|1,3,4,2,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,11,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,2,5,7,11,4,9,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,11,4,9,13,21,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1
|1,3,4,2,5,7,11,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,4,2,1,0)3(11,*10,4,3,2,1,0)4(12,11,10,4)2(13,12,11,10,4)3(14,*13,12,11,10,4)3
|1,3,4,2,5,7,11,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,11,10,5)2(13,12,11,10,5)3(14,*13,12,11,10,5)3
|1,3,4,2,5,7,11,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,4)1
|1,3,4,2,5,7,11,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,11,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,10,5,4)2(12,11,10,5,4)3(13,*12,11,10,5,4)3
|1,3,4,2,5,7,11,10,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2
|1,3,4,2,5,7,11,10,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,10,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3(16,12,11,10)2
|1,3,4,2,5,7,11,10,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,6,5,4)3
|1,3,4,2,5,7,11,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3
|1,3,4,2,5,7,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,11,10,7)2(13,12,11,10,7)3(14,*13,12,11,10,7)3
|1,3,4,2,5,7,11,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3
|1,3,4,2,5,7,11,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,10,8)1
|1,3,4,2,5,7,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,11,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,11,10,8)2(13,12,11,10,8)3(14,*13,12,11,10,8)3(15,13,11,10,8)3(16,*15,13,12,11,10,8)4
|1,3,4,2,5,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*11,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,7,6)1
|1,3,4,2,5,7,12,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,12,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,2,1,0)3
|1,3,4,2,5,7,12,14,11,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,12,14,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,12,16,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,9,8)1
|1,3,4,2,5,7,12,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,12,16,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4
|1,3,4,2,5,7,12,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,12,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*15,*14,12,11,10,9,8)4
|1,3,4,2,5,7,12,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,11,10)1
|1,3,4,2,5,7,12,16,25,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,2,5,7,12,16,25,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4
|1,3,4,2,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,1,0)1(9,8,1,0)2(10,9,8)1(11,10,8,1,0)3(12,*11,10,9,8,1,0)4(13,*12,*11,10,9,8,1,0)4
|1,3,4,2,5,8,4,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,8,4,9,14,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4
|1,3,4,2,5,8,4,9,14,6,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1
|1,3,4,2,5,8,4,9,14,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1(17,16,9,8)2(18,17,16)1(1918,16,9,8)3(20,*19,18,17,16,9,8)4(21,*20,*19,*18,17,16,9,8)4
|1,3,4,2,5,8,4,9,14,7,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,8,4,9,14,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,8,4,9,14,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1(10,9,2,1,0)3(11,*10,9,8,2,1,0)3(12,*11,*10,9,8,2,1,0)4
|1,3,4,2,5,8,4,9,14,8,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,33
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,72
|-
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|1,3,4,2,5,8,4,9,14,8,17,26,16,33,50
|-
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|1,3,4,2,5,8,5
|-
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|1,3,4,2,5,8,5,8
|-
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|1,3,4,2,5,8,7
|-
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|1,3,4,2,5,8,7,5
|-
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|1,3,4,2,5,8,7,5,7,12
|-
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|1,3,4,2,5,8,7,5,7,12,17
|-
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|1,3,4,2,5,8,7,5,7,12,17,12
|-
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|1,3,4,2,5,8,7,5,8
|-
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|1,3,4,2,5,8,7,10
|-
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|1,3,4,2,5,8,7,10,5
|-
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|1,3,4,2,5,8,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1
|1,3,4,2,5,8,7,12
|-
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|1,3,4,2,5,8,7,12,17
|-
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|1,3,4,2,5,8,7,12,17,11
|-
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|1,3,4,2,5,8,8
|-
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|1,3,4,2,5,8,10
|-
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|1,3,4,2,5,8,10,5
|-
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|1,3,4,2,5,8,11
|-
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|1,3,4,2,5,8,11,14
|-
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|1,3,4,2,5,9
|-
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|1,3,4,2,5,9,4,9,14
|-
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|1,3,4,2,5,9,4,9,14,19
|-
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|1,3,4,2,5,9,4,9,15
|-
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|1,3,4,2,5,9,4,9,15,8,17
|-
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|1,3,4,2,5,9,4,9,15,9
|-
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|1,3,4,2,5,9,4,9,16
|-
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|1,3,4,2,5,9,4,9,16,8,17
|-
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|1,3,4,2,5,9,4,9,16,8,17,26
|-
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|1,3,4,2,5,9,4,9,16,8,17,27
|-
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|1,3,4,2,5,9,4,9,16,8,17,28
|-
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|1,3,4,2,5,9,4,9,16,8,17,28,12
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50,67
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,51
|-
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|1,3,4,2,5,9,4,9,16,8,17,29,16,33,52
|-
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|1,3,4,3
|}

iBLP

2026-04-25T14:24:07Z

Baixie01000a7：

BHM分析Part5：ψ(I)~SRO

2026-02-27T07:02:43Z

Baixie01000a7：

本条目展示[[BHM]]分析的第五部分。使用<math>MOCF</math>进行对照

<nowiki>\begin{align}\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I+\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)=\psi(I+\psi_I(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)=\psi(I+\psi_I(\psi_I(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)=\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(I+\Omega_{\psi_I(I)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(2,0)(2,1)=\psi(I+\Omega_{\psi_I(I)+1}^{\Omega_{\psi_I(I)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,0)(6,1)(6,0)(7,0)(6,1)(4,0)(4,1)=\psi(I+\Omega_{\Omega_{\psi_I(I)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I+\psi_I(I+1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(I+\psi_I(I+2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I+\psi_I(I+\psi_I(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(I+\psi_I(I)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I\times3)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(I\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I\times\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^3)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)=\psi(I^\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I^{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)=\psi(I^{I^\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^{I^I}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I^2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I^I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)=\psi(\Omega_{I+1}^\Omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I+1}^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I+1}^{I}\times\omega+\Omega_{I+1}^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega^\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,0)=\psi(\Omega_{I+1}^{I}\times\psi(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)=\psi(\Omega_{I+1}^{I}\times\Omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{I+1}^{I}\times\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^{I}\times I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^I\times\psi_{\Omega_{I+1}}(\Omega_{I+1}^{I}\times I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(\Omega_{I+1}^{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I+1}^{\Omega_{I+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{I+1}^{\Omega_{I+1}}\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+2}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I+2}^{\Omega_{I+2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I+\omega\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,0)=\psi(\Omega_{I+\omega^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(\Omega_{I+\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(\Omega_{I+\Omega_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I\times3})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\Omega_{I\times\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I\times2)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I\times\omega)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^{I+1})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^{\Omega_{I+1}})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\omega})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,0)(4,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\Omega})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,1)(5,0)(6,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\Omega})})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I+2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)=\psi(\Omega_{\Omega_{I+\omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)=\psi(\Omega_{\Omega_{I+\Omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\Omega_{I\times2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(\Omega_{\Omega_{I\times\omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)(4,0)=\psi(\Omega_{\Omega_{\psi_{\Omega_{I+1}}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)=\psi(\Omega_{\Omega_{\Omega_{I+1}}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_2}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,1)(3,1)=\psi(\psi_{I_2}(0)+\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(0)+I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)=\psi(\psi_{I_2}(0)+\Omega_{I+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I_2}(0)\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)=\psi(\psi_{I_2}(0)\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{\psi_{I_2}(0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)=\psi(\Omega_{\psi_{I_2}(0)+1}^{\Omega_{\psi_{I_2}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\psi_{I_2}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{\psi_{I_2}(0)+1}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,1)(5,0)(6,0)(5,0)(6,1)(5,1)(4,0)(4,1)=\psi(\Omega_{\Omega_{\psi_{I_2}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\psi_{I_2}(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\psi_{I_2}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_2^{I_2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I_2+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I_2+1}^{\Omega_{I_2+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I_2+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(\Omega_{I_2+\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I_2+I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I_2\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I_2+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\Omega_{\Omega_{I_2+1}}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_3}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_4}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_\omega+I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)=\psi(I_\omega\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega^{I_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I_\omega+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)=\psi(\Omega_{I_{\omega}+1}^{\Omega_{I_{\omega}+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{\omega+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_{\omega\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)=\psi(I_{\omega^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)(2,0)=\psi(I_{\omega^\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)(3,0)=\psi(I_{\psi(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(I_{\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(I_{\Omega_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,1)(3,1)=\psi(I_{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,1)(2,1)=\psi(I_{I_2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_{I_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)=\psi(I_{I_\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{I_I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I(1,0)}(0)\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{\psi_{I(1,0)}(0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)=\psi(\Omega_{\psi_{I(1,0)}(0)+1}^{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)=\psi(\Omega_{\psi_{I(1,0)}(0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{\psi_{I(1,0)}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{\psi_{I(1,0)}(0)})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{\psi_{I(1,0)}(0)+1})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)=\psi(\Omega_{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_{\psi_{I(1,0)}(0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_{\psi_{I(1,0)}(0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{\psi_{I(1,0)}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(I_{\psi_{I(1,0)}(0)\times\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{I})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)=\psi(I_{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)(4,0)(5,0)(4,1)=\psi(I_{I_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I(1,0)}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I(1,0)}(2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\psi_{I(1,0)}(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I(1,0)}(\psi_{I(1,0)}(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0)^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)=\psi(I(1,0)^{\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0)^{I(1,0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{I(1,0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I(1,0)+1}^{\Omega_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0)+2}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_{I(1,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_{I(1,0)+I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_{I_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,2)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(1,\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(2,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(3,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)=\psi(\Omega_{I(\omega,0)+1}^{\Omega_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(\omega,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,I(\omega,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,2))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,I(\omega+1,0)+1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+1,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(\omega+1,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+2,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega\times3,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega^2+\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^2\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega^3,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega^3\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^4,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(2,0)=\psi(I(\omega^\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(2,0)(2,0)=\psi(I(\omega^{\omega^\omega},0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(3,0)=\psi(I(\psi(0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)=\psi(I(\Omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(I(\Omega_\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(I,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(I(1,0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)=\psi(I(I(\omega,0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)(2,0)(3,1)(3,0)(4,0)(4,0)=\psi(I(I(I(\omega,0),0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(3,0)(2,1)=\psi(\psi_{I(1,0,0)}(1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I(1,0,0)+1}^{\Omega_{I(1,0,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,I(1,0,0)+1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(I(1,0,1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(1,0,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(1,\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(3,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0,0,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0,0,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,I(1,0,0,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,I(1,0,0,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,0,1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,1,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0,0,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)=\psi(I(1@\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1@I))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)(3,0)=\psi(I(1@I(1@\omega)))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1@(1,0))}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1@(1@(1,0)))}(0))\\&(0,0)(1,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{M+1}}(0))\end{align}</nowiki>
[[分类:分析]]

DEN

2026-02-25T15:49:43Z

Baixie01000a7：已将重定向目标从iblp更改为iBLP

#REDIRECT [[iBLP]]

Googolism - Part 6

2026-02-25T15:23:31Z

Baixie01000a7：

【[[Googolism - Part 5|更小]] | [[Googolism|主页]] | 更大】

== Binary phi level ==

=== Part 6.1: <math>f_{\zeta_0}^2(10)</math> ~ <math>f_{\varepsilon_{\zeta_0+1}}^2(10)</math> ===

* Grand tethracross, E100#^^##100#2
* Grand Berlin Wall, E100#^^##100,000,000#2
* '''Fish number 6''', <math>\approx f_{\zeta_0+1}(63)</math>
* Grangol-carta-tethracross, E100#^^##100#100
* Godgahlah-carta-tethracross, E100#^^##100#^#100
* Tethrathoth-carta-tethracross, E100#^^##100#^^#100
* Tethriterator-carta-tethracross, E100#^^##100#^^#>#100
* Tethracross-by-deuteron, E100#^^##100#^^##100
* Tethracross-by-triton, E100#^^##100#^^##100#^^##100
* Tethracross-by-teterton, E100#^^##*#5
* Tethracross-by-pepton, E100#^^##*#6
* Tethracross-by-exton, E100#^^##*#7
* Tethracross-by-epton, E100#^^##*#8
* Tethracross-by-ogdon, E100#^^##*#9
* Tethracross-by-enton, E100#^^##*#10
* Tethracross-by-dekaton, E100#^^##*#11
* Deutero-tethrinoocross, {100,100[1\1\2]1[1\1\2]2}
* Deutero-tethracross, E100#^^##*#^^##100
* Trito-tethracross, E100#^^##*#^^##*#^^##100
* Teterto-tethracross, E100#^^##*#^^##*#^^##*#^^##100
* Pepto-tethracross, E100(#^^##)^#5
* Exto-tethracross, E100(#^^##)^#6
* Epto-tethracross, E100(#^^##)^#7
* Ogdo-tethracross, E100(#^^##)^#8
* Ento-tethracross, E100(#^^##)^#9
* Dekato-tethracross, E100(#^^##)^#10
* Isosto-tethracross, E100(#^^##)^#20
* Trianto-tethracross, E100(#^^##)^#30
* Saranto-tethracross, E100(#^^##)^#40
* Peninto-tethracross, E100(#^^##)^#50
* Exinto-tethracross, E100(#^^##)^#60
* Ebdominto-tethracross, E100(#^^##)^#70
* Ogdonto-tethracross, E100(#^^##)^#80
* Eneninto-tethracross, E100(#^^##)^#90
* Tethrinoocruxifact, {100,100[2\1\2]2}
* Tethracruxifact / hecato-tethracross, E100(#^^##)^#100
* Grideutertethrinoocross, {100,100[3\1\2]2}
* Grideutertethracross, E100(#^^##)^##100
* Kubicutethracross, E100(#^^##)^###100
* Quarticutethracross, E100(#^^##)^####100
* Quinticutethracross, E100(#^^##)^#^#5
* Sexticutethracross, E100(#^^##)^#^#6
* Septicutethracross, E100(#^^##)^#^#7
* Octicutethracross, E100(#^^##)^#^#8
* Nonicutethracross, E100(#^^##)^#^#9
* Decicutethracross, E100(#^^##)^#^#10
* Centicutethracross / Tethracruxigodgathor, E100(#^^##)^#^#100
* Tethracross-ad-gridgahlahium, E100(#^^##)^#^##100
* Tethracross-ad-kubikahlahium, E100(#^^##)^#^###100
* Tethracross-ad-quarticahlahium, E100(#^^##)^#^####100
* Tethracross-ad-godgathorium, E100(#^^##)^#^#^#100
* Tethracross-ad-godtotholium, E100(#^^##)^#^#^#^#100
* Tethracross-ad-godtertolium, E100(#^^##)^#^#^#^#^#100
* Tethracross-ad-godtopolium, E100(#^^##)^#^^#6
* Tethracross-ad-godhathorium, E100(#^^##)^#^^#7
* Tethracross-ad-godheptolium, E100(#^^##)^#^^#8
* Tethracross-ad-godoctolium, E100(#^^##)^#^^#9
* Tethracross-ad-godentolium, E100(#^^##)^#^^#10
* Tethracross-ad-goddekatholium, E100(#^^##)^#^^#11
* Tethracross-ad-tethrathothium / Tethracruxitethrathoth, E100(#^^##)^#^^#100
* Tethracross-ad-Monster-Giantium, E100(#^^##)^(#^^#)^(#^^#)^#100
* Tethracross-ad-terrible-tethrathothium, E100(#^^##)^(#^^#)^^#100
* Tethracross-ad-terrible-terrible-tethrathothium, E100(#^^##)^((#^^#)^^#)^^#100
* Tethracross-ad-tethriteratorium, E100(#^^##)^#^^#>#100
* Tethracross-ad-tethriditeratorium, E100(#^^##)^#^^#>(#+#)100
* Tethracross-ad-tethraspatialatorium, E100(#^^##)^#^^#>#^#100
* Tethracross-ad-dustaculated-tethrathothium, E100(#^^##)^#^^#>#^^#100
* Tethracross-ad-tristaculated-tethrathothium, E100(#^^##)^#^^#>#^^#>#^^#100
* Tethracross-ad-tetrastaculated-tethrathothium, E100(#^^##)^#^^#>#^^#>#^^#>#^^#100
* Tethracross-ad-pentastaculated-tethrathothium, E100(#^^##)^#^^##5
* Tethracross-ad-hexastaculated-tethrathothium, E100(#^^##)^#^^##6
* Tethracross-ad-heptastaculated-tethrathothium, E100(#^^##)^#^^##7
* Tethracross-ad-octastaculated-tethrathothium, E100(#^^##)^#^^##8
* Tethracross-ad-ennastaculated-tethrathothium, E100(#^^##)^#^^##9
* Tethracross-ad-dekastaculated-tethrathothium, E100(#^^##)^#^^##10
* Dutetrated-tethracross, E100(#^^##)^(#^^##)100
* Tritetrated-tethracross, E100(#^^##)^(#^^##)^(#^^##)100
* Quadratetrated-tethracross, E100(#^^##)^(#^^##)^(#^^##)^(#^^##)100
* Quinquatetrated-tethracross, E100(#^^##)^^#5
* Sexatetrated-tethracross, E100(#^^##)^^#6
* Septatetrated-tethracross, E100(#^^##)^^#7
* Octatetrated-tethracross, E100(#^^##)^^#8
* Nonatetrated-tethracross, E100(#^^##)^^#9
* Decatetrated-tethracross, E100(#^^##)^^#10
* Terrible tethracross, E100(#^^##)^^#100

=== Part 6.2: <math>f_{\varepsilon_{\zeta_0+1}}^2(10)</math> ~ <math>f_{\zeta_1}^2(10)</math> ===

* Dutetrated-terrible-tethracross, E100((#^^##)^^#)^((#^^##)^^#)100
* Terrible terrible tethracross, E100((#^^##)^^#)^^#100
* Terrible terrible terrible tethracross, E100(((#^^##)^^#)^^#)^^#100
* Quadruple-terrible tethracross, E100((((#^^##)^^#)^^#)^^#)^^#100
* Quintuple-terrible tethracross, E100(#^^##)^^#>#5
* Tethriterated-tethracross / hundred-ex-terrible tethracross, E100(#^^##)^^#>#100
* Hundred-ex-terrible territethracross, E100(#^^##)^^#>#101
* Tethrathoth-ex-terrible tethracross, E100(#^^##)^^#>#(E100#^^#100)
* Tethracross-ex-terrible tethracross, E100(#^^##)^^#>#(E100#^^##100)
* Grand tethriterated-tethracross, E100(#^^##)^^#>#100#2
* Deutero-tethriterated-tethracross, E100(#^^##)^^#>#*(#^^##)^^#>#100
* Dutetrated-tethriterated-tethracross, E100((#^^##)^^#>#)^((#^^##)^^#>#)100
* Tethriditerated-tethracross, E100(#^^##)^^#>(#+#)100
* Tethritriterated-tethracross, E100(#^^##)^^#>(#+#+#)100
* Tethriquaditerated-tethracross, E100(#^^##)^^#>(#+#+#+#)100
* Tethriquiditerated-tethracross, E100(#^^##)^^#>##5
* Tethrisiditerated-tethracross, E100(#^^##)^^#>##6
* Tethrisepiterated-tethracross, E100(#^^##)^^#>##7
* Tethri-ogditerated-tethracross, E100(#^^##)^^#>##8
* Tethri-noniterated-tethracross, E100(#^^##)^^#>##9
* Tethri-deciterated-tethracross, E100(#^^##)^^#>##10
* Tethrigriditerated-tethracross, E100(#^^##)^^#>##100
* Tethricubiculated-tethracross, E100(#^^##)^^#>###100
* Tethriquarticulated-tethracross, E100(#^^##)^^#>####100
* Tethriquinticulated-tethracross, E100(#^^##)^^#>#^#5
* Tethrisexticulated-tethracross, E100(#^^##)^^#>#^#6
* Tethrisepticulated-tethracross, E100(#^^##)^^#>#^#7
* Tethri-octiculated-tethracross, E100(#^^##)^^#>#^#8
* Tethrinoniculated-tethracross, E100(#^^##)^^#>#^#9
* Tethrideciculated-tethracross, E100(#^^##)^^#>#^#10
* Tethrispatialated-tethracross, E100(#^^##)^^#>#^#100
* Tethrispatial-squarediterated-tethracross, E100(#^^##)^^#>(#^#*#^#)100
* Tethrideuterspatialated-tethracross, E100(#^^##)^^#>#^##100
* Tethritritospatialated-tethracross, E100(#^^##)^^#>#^###100
* Tethritetertospatialated-tethracross, E100(#^^##)^^#>#^####100
* Tethripeptospatialated-tethracross, E100(#^^##)^^#>#^#^#5
* Tethriextospatialated-tethracross, E100(#^^##)^^#>#^#^#6
* Tethrieptospatialated-tethracross, E100(#^^##)^^#>#^#^#7
* Tethriogdospatialated-tethracross, E100(#^^##)^^#>#^#^#8
* Tethrientospatialated-tethracross, E100(#^^##)^^#>#^#^#9
* Tethridekatospatialated-tethracross, E100(#^^##)^^#>#^#^#10
* Tethrisuperspatialated-tethracross, E100(#^^##)^^#>#^#^#100
* Gralgathor-turreted-tethritertethracross, E100(#^^##)^^#>#^#^##100
* Tethriquadratetratediterated-tethracross, E100(#^^##)^^#>#^#^#^#100
* Tethriquintatetratediterated-tethracross, E100(#^^##)^^#>#^^#5
* Tethrisextatetratediterated-tethracross, E100(#^^##)^^#>#^^#6
* Tethriseptatetratediterated-tethracross, E100(#^^##)^^#>#^^#7
* Tethrioctatetratediterated-tethracross, E100(#^^##)^^#>#^^#8
* Tethrinonatetratediterated-tethracross, E100(#^^##)^^#>#^^#9
* Tethridecatetratediterated-tethracross, E100(#^^##)^^#>#^^#10
* Tethrastaculated-tethritertethracross / tethricentatetratediterated-tethracross, E100(#^^##)^^#>#^^#100
* Territethrastaculated-tethritertethracross, E100(#^^##)^^#>(#^^#)^^#100
* Tethriterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#100
* Tethriditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#)100
* Tethritriterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#+#)100
* Tethriquaditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#+#+#)100
* Tethrigriditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>##100
* Tethricubiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>###100
* Tethriquartiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>####100
* Tethrispatialiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^#100
* Tethrisuperspatialiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^#^#100
* Tethriquadratetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#4
* Tethriquintatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#5
* Tethrisextatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#6
* Tethriseptatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#7
* Tethrioctatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#8
* Tethrinonatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#9
* Tethridecatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#10
* Dustaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#100
* Tristaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#>#^^#100
* Tetrastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##4
* Pentastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##5
* Sexastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##6
* Septastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##7
* Octastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##8
* Ennastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##9
* Dekastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##10
* Tethracrossturreted-tethritertethracross, E100(#^^##)^^#>#^^##100
* Deutero tethracross-turreted-tethritertethracross, E100(#^^##)^^#>#^^##*(#^^##)^^#>#^^##100
* Trito tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^#3
* Teterto tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^#4
* Dutetrated tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^((#^^##)^^#>#^^##)100
* Tritetrated tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^^#3
* Tethracruxifact-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^#100
* Tethracruxitethrathoth-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^(#^^#)100
* Dutetrated-tethracross-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^(#^^##)100
* Dustaculated-tethritertethracross / territethracrossturreted-tethritertethracross / tethritertethracrossturreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#100
* Tethriterated-tethracross-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>#100
* Tethracross-turreted-dustaculated-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>#^^##100
* Tristaculated-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>(#^^##)^^#100
* Tetrastaculated-tethritertethracross, E100(#^^##)^^##4
* Pentastaculated-tethritertethracross, E100(#^^##)^^##5
* Hexastaculated-tethritertethracross, E100(#^^##)^^##6
* Heptastaculated-tethritertethracross, E100(#^^##)^^##7
* Ogdastaculated-tethritertethracross, E100(#^^##)^^##8
* Ennastaculated-tethritertethracross, E100(#^^##)^^##9
* Dekastaculated-tethritertethracross, E100(#^^##)^^##10
* Secundotethrated-tethrinoocross, {100,100[1\1\3]2}
* Secundotethrated-tethracross, E100(#^^##)^^##100

=== Part 6.3: <math>f_{\zeta_1}^2(10)</math> ~ <math>f_{\eta_0}^2(10)</math> ===

* Deutero-secundotethrated-tethracross, E100(#^^##)^^##*(#^^##)^^##100
* Dutetrated-secundotethrated-tethracross, E100((#^^##)^^##)^((#^^##)^^##)100
* Terrible secundotethrated-tethracross, E100((#^^##)^^##)^^#100
* Tethriterated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#100
* Tethrispatialated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#^#100
* Tethracross-turreted-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#^^##100
* Tethraducross-turreted-secundotethrated-tethracross, E100((#^^##)^^##)^^#>(#^^##)^^##100
* Dustaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>((#^^##)^^##)^^#100
* Tristaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##3
* Quadrastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##4
* Quinquastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##5
* Sexastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##6
* Septastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##7
* Ogdastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##8
* Ennastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##9
* Dekastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##10
* Thrice-tethrinoosecunda, {100,100[1\1\4]2}
* Thrice-tethrasecunda, E100((#^^##)^^##)^^##100
* Terrible thrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^#100
* Tethriterated-thrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^#>#100
* Dustaculated-thrice-territethrasecunda, E100(((#^^##)^^##)^^##)^^#>(((#^^##)^^##)^^##)^^#100
* Quatrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^##100
* Quincice-tethrinoosecunda, {100,100[1\1\6]2}
* Quincice-tethrasecunda, E100#^^##>#5
* Sextice-tethrasecunda, E100#^^##>#6
* Septice-tethrasecunda, E100#^^##>#7
* Octice-tethrasecunda, E100#^^##>#8
* Nonice-tethrasecunda, E100#^^##>#9
* Decice-tethrasecunda, E100#^^##>#10
* Tethrinootercross, {100,100[1\1\1,2]2}
* Tethritercross / tethrasquared-iterator, E100#^^##>#100
* Tethrinooditercross, {100,100[1\1\1,3]2}
* Terrible tethritercross, E100(#^^##>#)^^#100
* Tethriterated-tethritercross, E100(#^^##>#)^^#>#100
* Terrisquared tethritercross, E100(#^^##>#)^^##100
* Tethriditercross, E100#^^##>(#+#)100
* Tethritritercross, E100#^^##>(#+#+#)100
* Tethriquaditercross, E100#^^##>(#+#+#+#)100
* Tethriquiditercross, E100#^^##>##5
* Tethrisiditercross, E100#^^##>##6
* Tethrisepitercross, E100#^^##>##7
* Tethri-ogditercross, E100#^^##>##8
* Tethrinonitercross, E100#^^##>##9
* Tethridecitercross, E100#^^##>##10
* Tethrigriditercross / tethrasquared-griditerator, E100#^^##>##100
* Tethricubiculcross / tethrasquared-cubiculator, E100#^^##>###100
* Tethriquarticulcross, E100#^^##>####100
* Tethriquinticulcross, E100#^^##>#^#5
* Tethrisexticulcross, E100#^^##>#^#6
* Tethrisepticulcross, E100#^^##>#^#7
* Tethri-octiculcross, E100#^^##>#^#8
* Tethrinoniculcross, E100#^^##>#^#9
* Tethrideciculcross, E100#^^##>#^#10
* Tethrispatialcross / tethrasquared-spatialator, E100#^^##>#^#100
* Tethrisuperspatialcross, E100#^^##>#^#^#100
* Tethritrimensionalcross, E100#^^##>#^#^#^#100
* Tethriquadramensionalcross, E100#^^##>#^^#5
* Tethriquintamensionalcross, E100#^^##>#^^#6
* Tethrisexamensionalcross, E100#^^##>#^^#7
* Tethrseptamensionalcross, E100#^^##>#^^#8
* Tethri-octamensionalcross, E100#^^##>#^^#9
* Tethrinonamensionalcross, E100#^^##>#^^#10
* Tethraidecamensionalcross, E100#^^##>#^^#11
* Tethraturreted-tethracross, E100#^^##>#^^#100
* Dustacutethraturreted-tethracross, E100#^^##>#^^#>#^^#100
* Tristacutethraturreted-tethracross, E100#^^##>#^^#>#^^#>#^^#100
* Tetrastacutethraturreted-tethracross, E100#^^##>#^^##4
* Pentastacutethraturreted-tethracross, E100#^^##>#^^##5
* Hexastacutethraturreted-tethracross, E100#^^##>#^^##6
* Heptastacutethraturreted-tethracross, E100#^^##>#^^##7
* Ogdastacutethraturreted-tethracross, E100#^^##>#^^##8
* Ennastacutethraturreted-tethracross, E100#^^##>#^^##9
* Uninzet, <math>f_{\zeta_{\zeta_0}}(10)</math>
* Dekastacutethraturreted-tethracross, E100#^^##>#^^##10
* Dustaculated-tethracross, E100#^^##>#^^##100
* Terrible dustaculated-tethracross, E100(#^^##>#^^##)^^#100
* Tethriterated dustaculated-tethracross, E100(#^^##>#^^##)^^#>#100
* Terrisecunded dustaculated-tethracross / Terrisquared dustaculated-tethracross, E100(#^^##>#^^##)^^##100
* Double terrisecunded dustaculated-tethracross / Terrisquared terrisquared dustaculated-tethracross, E100((#^^##>#^^##)^^##)^^##100
* Hundred-ex-terrisecunded dustaculated-tethracross / Terrisquarediter-dustaculated-tethracross, E100#^^##>(#^^##+#)100
* Tethracross-by-deuteron-turreted-tethracross, E100#^^##>(#^^##+#^^##)100
* Tethracross-by-gugold-turreted-tethracross, E100#^^##>(#^^##*#)100
* Deutertethracross-turreted-tethracross, E100#^^##>(#^^##*#^^##)100
* Tethracruxifact-turreted-tethracross, E100#^^##>(#^^##)^#100
* Grideutertethracross-turreted-tethracross, E100#^^##>(#^^##)^##100
* Tethracruxigodgathor-turreted-tethracross, E100#^^##>(#^^##)^#^#100
* Terrible-tethracross-turreted-tethracross, E100#^^##>(#^^##)^^#100
* Secundotethrated-tethracross-turreted-tethracross, E100#^^##>(#^^##)^^##100
* Thrice-tethrasecunda-turreted-tethracross, E100#^^##>((#^^##)^^##)^^##100
* Quatrice-tethrasecunda-turreted-tethracross, E100#^^##>(((#^^##)^^##)^^##)^^##100
* Tethritercross-turreted-tethracross, E100#^^##>#^^##>#100
* Tethriditercross-turreted-tethracross, E100#^^##>#^^##>(#+#)100
* Tethrigriditercross-turreted-tethracross, E100#^^##>#^^##>##100
* Tethrispatialcross-turreted-tethracross, E100#^^##>#^^##>#^#100
* Tethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#100
* Territethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^#)^^#100
* Tethriterturreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#>#100
* Dustaculated-tethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#>#^^#100
* Binzet, <math>f_{\zeta_{\zeta_{\zeta_0}}}(10)</math>
* Tristaculated-tethracross, E100#^^##>#^^##>#^^##100
* Terrisquared tristaculated-tethracross, E100(#^^##>#^^##>#^^##)^^##100
* Terrisquared-dustaculated-tethracross-turreted-tethracross, E100#^^##>(#^^##>#^^##)^^##100
* Tethracruxifact-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^#100
* Territethracross-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^^#100
* Secundotethrated-tethracross-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^^##100
* Thrice-tethrasecunda-turreted-dustaculated-tethracross, E100#^^##>#^^##>((#^^##)^^##)^^##100
* Tethritercross-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^##>#100
* Trinzet, <math>f_{\zeta_{\zeta_{\zeta_{\zeta_0}}}}(10)</math>
* Tetrastaculated-tethracross, E100#^^##>#^^##>#^^##>#^^##100
* Tethritercross-turreted-tristaculated-tethracross, E100#^^##>#^^##>#^^##>#^^##>#100
* Quadrinzet, <math>f_{\eta_0[5]}(10)</math>
* Pentastaculated-tethracross, E100#^^###5
* Quintinzet, <math>f_{\eta_0[6]}(10)</math>
* Sexastaculated-tethracross, E100#^^###6
* Sextinzet, <math>f_{\eta_0[7]}(10)</math>
* Septastaculated-tethracross, E100#^^###7
* Septinzet, <math>f_{\eta_0[8]}(10)</math>
* Ogdastaculated-tethracross, E100#^^###8
* Octinzet, <math>f_{\eta_0[9]}(10)</math>
* Ennastaculated-tethracross, E100#^^###9
* Noninzet / triphi, <math>f_{\eta_0}(10)</math>
* Dekastaculated-tethracross, E100#^^###10
* Dekinzet, <math>f_{\eta_0[11]}(10)</math>
* Icosastaculated-tethracross, E100#^^###20
* Triantastaculated-tethracross, E100#^^###30
* Sarantastaculated-tethracross, E100#^^###40
* Penintastaculated-tethracross, E100#^^###50
* Exintastaculated-tethracross, E100#^^###60
* Ebdomintastaculated-tethracross, E100#^^###70
* Ogdontastaculated-tethracross, E100#^^###80
* Enenintastaculated-tethracross, E100#^^###90
* Tethrinoocubor, {100,100[1\1\1\2]2}
* Tethracubor / tethratertia, E100#^^###100
* Hektinzet, <math>f_{\eta_0[101]}(10)</math>
* Kilinzet, <math>f_{\eta_0[1001]}(10)</math>
* Meginzet, <math>f_{\eta_0[10^6+1]}(10)</math>
* Giginzet, <math>f_{\eta_0[10^9+1]}(10)</math>
* Terinzet, <math>f_{\eta_0[10^{12}+1]}(10)</math>
* Petinzet, <math>f_{\eta_0[10^{15}+1]}(10)</math>
* Exinzet, <math>f_{\eta_0[10^{18}+1]}(10)</math>
* Zettinzet, <math>f_{\eta_0[10^{21}+1]}(10)</math>
* Yottinzet, <math>f_{\eta_0[10^{24}+1]}(10)</math>

=== Part 6.4: <math>f_{\eta_0}^2(10)</math> ~ <math>f_{\varepsilon_{\eta_0+1}}^2(10)</math> ===

* Grand tethracubor, E100#^^###100#2
* Grangol-carta-tethracubor, E100#^^###100#100
* Grand grangol-carta-tethracubor, E100#^^###100#100#2
* Godgahlah-carta-tethracubor, E100#^^###100#^#100
* Tethrathoth-carta-tethracubor, E100#^^###100#^^#100
* Tethriterator-carta-tethracubor, E100#^^###100#^^#>#100
* Tethracross-carta-tethracubor, E100#^^###100#^^##100
* Tethrinoocubor-by-deuteron, {100,100[1\1\1\2]3}
* Tethracubor-by-deuteron, E100#^^###100#^^###100
* Tethracubor-by-triton, E100#^^###100#^^###100#^^###100
* Tethracubor-by-teterton, E100#^^###*#5
* Tethracubor-by-pepton, E100#^^###*#6
* Tethracubor-by-exton, E100#^^###*#7
* Tethracubor-by-epton, E100#^^###*#8
* Tethracubor-by-ogdon, E100#^^###*#9
* Tethracubor-by-enton, E100#^^###*#10
* Tethracubor-by-dekaton, E100#^^###*#11
* Tethrinoocuborgugold, {100,100[1\1\1\2]100}
* Tethracubor-by-hyperion, E100#^^###*#100
* Tethracubor-by-hecaton, E100#^^###*#101
* Tethracubor-by-deutero-hyperion, E100#^^###*##100
* Tethracubor-by-trito-hyperion, E100#^^###*###100
* Tethracubor-by-teterto-hyperion, E100#^^###*####100
* Tethracubor-by-godgahlah, E100#^^###*#^#100
* Tethracubor-by-gridgahlah, E100#^^###*#^##100
* Tethracubor-by-godgathor, E100#^^###*#^#^#100
* Tethracubor-by-godtothol, E100#^^###*#^#^#^#100
* Tethracubor-by-tethrathoth, E100#^^###*#^^#100
* Tethracubor-by-Monster-Giant, E100#^^###*(#^^#)^(#^^#)^#100
* Tethracubor-by-terrible-tethrathoth, E100#^^###*(#^^#)^^#100
* Tethracubor-by-Behemoth-Giant, E100#^^###*(#^^#>2)^(#^^#>2)^#100
* Tethracubor-by-terrible-terrible-tethrathoth, E100#^^###*#^^#>#3
* Tethracubor-by-Trihemoth-Giant, E100#^^###*(#^^#>3)^(#^^#>3)^#100
* Tethracubor-by-tethriterator, E100#^^###*#^^#>#100
* Tethracubor-by-dustaculated-tethrathoth, E100#^^###*#^^#>#^^#100
* Tethracubor-by-tethracross, E100#^^###*#^^##100
* Tethracubor-by-tethritercross, E100#^^###*#^^##>#100
* Tethracubor-by-dustaculated-tethracross, E100#^^###*#^^##>#^^##100
* Deutero-tethracubor, E100#^^###*#^^###100
* Trito-tethracubor, E100#^^###*#^^###*#^^###100
* Teterto-tethracubor, E100#^^###*#^^###*#^^###*#^^###100
* Pepto-tethracubor, E100(#^^###)^#5
* Exto-tethracubor, E100(#^^###)^#6
* Epto-tethracubor, E100(#^^###)^#7
* Ogdo-tethracubor, E100(#^^###)^#8
* Ento-tethracubor, E100(#^^###)^#9
* Dekato-tethracubor, E100(#^^###)^#10
* Isosto-tethracubor, E100(#^^###)^#20
* Trianto-tethracubor, E100(#^^###)^#30
* Saranto-tethracubor, E100(#^^###)^#40
* Peninto-tethracubor, E100(#^^###)^#50
* Exinto-tethracubor, E100(#^^###)^#60
* Ebdominto-tethracubor, E100(#^^###)^#70
* Ogdonto-tethracubor, E100(#^^###)^#80
* Eneninto-tethracubor, E100(#^^###)^#90
* Tethracuborfact / hecato-tethracubor, E100(#^^###)^#100
* Grideutertethracubor, E100(#^^###)^##100
* Kubicutethracubor, E100(#^^###)^###100
* Quarticutethracubor, E100(#^^###)^####100
* Quinticutethracubor, E100(#^^###)^#^#5
* Sexticutethracubor, E100(#^^###)^#^#6
* Septicutethracubor, E100(#^^###)^#^#7
* Octicutethracubor, E100(#^^###)^#^#8
* Nonicutethracubor, E100(#^^###)^#^#9
* Decicutethracubor, E100(#^^###)^#^#10
* Tethracuborgodgathored, E100(#^^###)^#^#100
* Tethracuborgralgathored, E100(#^^###)^#^##100
* Tethracuborgodtotholed, E100(#^^###)^#^#^#100
* Tethracubor-isptethrathoth, E100(#^^###)^#^^#100
* Tethracubor-isptethriterator, E100(#^^###)^#^^#>#100
* Tethracubor-isptethracross, E100(#^^###)^#^^##100
* Tethracubor-isptethritercross, E100(#^^###)^#^^##>#100
* Dutetrated-tethracubor / tethracubor-isptethracubor, E100(#^^###)^(#^^###)100
* Monster-Tethracubor, E100(#^^###)^(#^^###)^#100
* Tritetrated-tethracubor, E100(#^^###)^(#^^###)^(#^^###)100
* Quadratetrated-tethracubor, E100(#^^###)^^#4
* Quinquatetrated-tethracubor, E100(#^^###)^^#5
* Sexatetrated-tethracubor, E100(#^^###)^^#6
* Septatetrated-tethracubor, E100(#^^###)^^#7
* Octatetrated-tethracubor, E100(#^^###)^^#8
* Nonatetrated-tethracubor, E100(#^^###)^^#9
* Decatetrated-tethracubor, E100(#^^###)^^#10
* Vigintatetrated-tethracubor, E100(#^^###)^^#20
* Trigintatetrated-tethracubor, E100(#^^###)^^#30
* Quadragintatetrated-tethracubor, E100(#^^###)^^#40
* Quinquagintatetrated-tethracubor, E100(#^^###)^^#50
* Sexagintatetrated-tethracubor, E100(#^^###)^^#60
* Septuagintatetrated-tethracubor, E100(#^^###)^^#70
* Octogintatetrated-tethracubor, E100(#^^###)^^#80
* Nonagintatetrated-tethracubor, E100(#^^###)^^#90
* Terrible tethracubor, E100(#^^###)^^#100

=== Part 6.5: <math>f_{\varepsilon_{\eta_0+1}}^2(10)</math> ~ <math>f_{\eta_1}^2(10)</math> ===

* Terrible terrible tethracubor, E100((#^^###)^^#)^^#100
* Tethriterated-tethracubor / hundred-ex-terrible tethracubor, E100(#^^###)^^#>#100
* Dustaculated-territethracubor, E100(#^^###)^^#>(#^^###)^^#100
* Tristaculated-territethracubor, E100(#^^###)^^#>(#^^###)^^#>(#^^###)^^#100
* Tetrastaculated-territethracubor, E100(#^^###)^^##4
* Pentastaculated-territethracubor, E100(#^^###)^^##5
* Hexastaculated-territethracubor, E100(#^^###)^^##6
* Heptastaculated-territethracubor, E100(#^^###)^^##7
* Ogdastaculated-territethracubor, E100(#^^###)^^##8
* Ennastaculated-territethracubor, E100(#^^###)^^##9
* Dekastaculated-territethracubor, E100(#^^###)^^##10
* Icosastaculated-territethracubor, E100(#^^###)^^##20
* Triantastaculated-territethracubor, E100(#^^###)^^##30
* Sarantastaculated-territethracubor, E100(#^^###)^^##40
* Penintastaculated-territethracubor, E100(#^^###)^^##50
* Exintastaculated-territethracubor, E100(#^^###)^^##60
* Ebdomintastaculated-territethracubor, E100(#^^###)^^##70
* Ogdontastaculated-territethracubor, E100(#^^###)^^##80
* Enenintastaculated-territethracubor, E100(#^^###)^^##90
* Terrisquared-tethracubor / hectastaculated-territethracubor, E100(#^^###)^^##100
* Terrible terrisquared-tethracubor, E100((#^^###)^^##)^^#100
* Territerated terrisquared-tethracubor, E100((#^^###)^^##)^^#>#100
* Double-terrisquared-tethracubor, E100((#^^###)^^##)^^##100
* Triple-terrisquared-tethracubor, E100(((#^^###)^^##)^^##)^^##100
* Quadruple-terrisquared-tethracubor, E100(#^^###)^^##>#4
* Quintuple-terrisquared-tethracubor, E100(#^^###)^^##>#5
* Sextuple-terrisquared-tethracubor, E100(#^^###)^^##>#6
* Septuple-terrisquared-tethracubor, E100(#^^###)^^##>#7
* Octuple-terrisquared-tethracubor, E100(#^^###)^^##>#8
* Nonuple-terrisquared-tethracubor, E100(#^^###)^^##>#9
* Decuple-terrisquared-tethracubor, E100(#^^###)^^##>#10
* Vigintuple-terrisquared-tethracubor, E100(#^^###)^^##>#20
* Trigintuple-terrisquared-tethracubor, E100(#^^###)^^##>#30
* Quadragintuple-terrisquared-tethracubor, E100(#^^###)^^##>#40
* Quinquagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#50
* Sexagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#60
* Septuagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#70
* Octogintuple-terrisquared-tethracubor, E100(#^^###)^^##>#80
* Nonagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#90
* Terrisquarediter-tethracubor / centuple-terrisquared-tethracubor, E100(#^^###)^^##>#100
* Dustaculated-terrisquared-tethracubor, E100(#^^###)^^##>(#^^###)^^##100
* Tristaculated-terrisquared-tethracubor, E100(#^^###)^^###3
* Tetrastaculated-terrisquared-tethracubor, E100(#^^###)^^###4
* Pentastaculated-terrisquared-tethracubor, E100(#^^###)^^###5
* Hexastaculated-terrisquared-tethracubor, E100(#^^###)^^###6
* Heptastaculated-terrisquared-tethracubor, E100(#^^###)^^###7
* Ogdastaculated-terrisquared-tethracubor, E100(#^^###)^^###8
* Ennastaculated-terrisquared-tethracubor, E100(#^^###)^^###9
* Dekastaculated-terrisquared-tethracubor, E100(#^^###)^^###10
* Icosastaculated-terrisquared-tethracubor, E100(#^^###)^^###20
* Triantastaculated-terrisquared-tethracubor, E100(#^^###)^^###30
* Sarantastaculated-terrisquared-tethracubor, E100(#^^###)^^###40
* Penintastaculated-terrisquared-tethracubor, E100(#^^###)^^###50
* Exintastaculated-terrisquared-tethracubor, E100(#^^###)^^###60
* Ebdomintastaculated-terrisquared-tethracubor, E100(#^^###)^^###70
* Ogdontastaculated-terrisquared-tethracubor, E100(#^^###)^^###80
* Enenintastaculated-terrisquared-tethracubor, E100(#^^###)^^###90
* Tethraducubor / hectastaculated-terrisquared-tethracubor, E100(#^^###)^^###100

=== Part 6.6: <math>f_{\eta_1}^2(10)</math> ~ <math>f_{\vartheta_{0}}^2(10)</math> ===

* Terrible tethraducubor, E100((#^^###)^^###)^^#100
* Terrisquared-tethraducubor, E100((#^^###)^^###)^^##100
* Tethratricubor, E100((#^^###)^^###)^^###100
* Tethratetracubor, E100(((#^^###)^^###)^^###)^^###100
* Tethrapentacubor, E100#^^###>#5
* Tethrahexacubor, E100#^^###>#6
* Tethraheptacubor, E100#^^###>#7
* Tethra-octacubor, E100#^^###>#8
* Tethra-ennacubor, E100#^^###>#9
* Tethradekacubor, E100#^^###>#10
* Tethra-endekacubor, E100#^^###>#11
* Tethra-dodekacubor, E100#^^###>#12
* Tethra-triadekacubor, E100#^^###>#13
* Tethra-tetradekacubor, E100#^^###>#14
* Tethra-pentadekacubor, E100#^^###>#15
* Tethra-hexadekacubor, E100#^^###>#16
* Tethra-heptadekacubor, E100#^^###>#17
* Tethra-octadekacubor, E100#^^###>#18
* Tethra-ennadekacubor, E100#^^###>#19
* Tethra-icosacubor, E100#^^###>#20
* Tethra-triantacubor, E100#^^###>#30
* Tethra-sarantacubor, E100#^^###>#40
* Tethra-penintacubor, E100#^^###>#50
* Tethra-exintacubor, E100#^^###>#60
* Tethra-ebdomintacubor, E100#^^###>#70
* Tethra-ogdontacubor, E100#^^###>#80
* Tethra-enenintacubor, E100#^^###>#90
* Tethritercubor / tethrahectacubor / tethracubiter, E100#^^###>#100
* Tethriditercubor, E100#^^###>(#+#)100
* Tethritritercubor, E100#^^###>(#+#+#)100
* Tethriquaditercubor, E100#^^###>(#+#+#+#)100
* Tethriquiditercubor, E100#^^###>##5
* Tethrisiditercubor, E100#^^###>##6
* Tethrisepitercubor, E100#^^###>##7
* Tethri-ogditercubor, E100#^^###>##8
* Tethrinonitercubor, E100#^^###>##9
* Tethridecitercubor, E100#^^###>##10
* Tethrivigintitercubor, E100#^^###>##20
* Tethritrigintitercubor, E100#^^###>##30
* Tethriquadragintitercubor, E100#^^###>##40
* Tethriquinquagintitercubor, E100#^^###>##50
* Tethrisexagintitercubor, E100#^^###>##60
* Tethriseptuagintitercubor, E100#^^###>##70
* Tethri-octogintitercubor, E100#^^###>##80
* Tethrinonagintitercubor, E100#^^###>##90
* Tethrigriditercubor / tethricentitercubor, E100#^^###>##100
* Tethricubiculcubor, E100#^^###>###100
* Tethriquarticulcubor, E100#^^###>####100
* Tethriquinticulcubor, E100#^^###>#^#5
* Tethrisexticulcubor, E100#^^###>#^#6
* Tethrisepticulcubor, E100#^^###>#^#7
* Tethri-octiculcubor, E100#^^###>#^#8
* Tethrinoniculcubor, E100#^^###>#^#9
* Tethrideciculcubor, E100#^^###>#^#10
* Tethriviginticulcubor, E100#^^###>#^#20
* Tethritriginticulcubor, E100#^^###>#^#30
* Tethriquadraginticulcubor, E100#^^###>#^#40
* Tethriquinquaginticulcubor, E100#^^###>#^#50
* Tethrisexaginticulcubor, E100#^^###>#^#60
* Tethriseptuaginticulcubor, E100#^^###>#^#70
* Tethri-octoginticulcubor, E100#^^###>#^#80
* Tethri-nonaginticulcubor, E100#^^###>#^#90
* Tethricenticulcubor / Tethrispatialcubor, E100#^^###>#^#100
* Gridgahlah-turreted-tethracubor / Tethrideuterspatialcubor, E100#^^###>#^##100
* Godgathor-turreted-tethracubor / Tethrisuperspatialcubor, E100#^^###>#^#^#100
* Godtothol-turreted-tethracubor, E100#^^###>#^#^#^#100
* Tethrathoth-turreted-tethracubor, E100#^^###>#^^#100
* Monster-Giant-turreted-tethracubor, E100#^^###>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethracubor, E100#^^###>(#^^#)^^#100
* Behemoth-Giant-turreted-tethracubor, E100#^^###>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethracubor, E100#^^###>((#^^#)^^#)^^#100
* Trihemoth-Giant-turreted-tethracubor, E100#^^###>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethracubor, E100#^^###>#^^#>#100
* Dustacultethrathoth-turreted-tethracubor, E100#^^###>#^^#>#^^#100
* Tethracross-turreted-tethracubor, E100#^^###>#^^##100
* Tethritercross-turreted-tethracubor, E100#^^###>#^^##>#100
* Godgahlah-turreted-tethracross-turreted-tethracubor / Tethrispatialcross-turreted-tethracubor, E100#^^###>#^^##>#^#100
* Tethrathoth-turreted-tethracross-turreted-tethracubor, E100#^^###>#^^##>#^^#100
* Dustacultethracross-turreted-tethracubor, E100#^^###>#^^##>#^^##100
* Uninet, <math>f_{\eta_{\eta_0}}(10)</math>
* Dustaculated-tethracubor, E100#^^###>#^^###100
* Terricubed dustaculated-tethracubor, E100(#^^###>#^^###)^^###100
* Tethraducubor-turreted-tethracubor, E100#^^###>(#^^###)^^###100
* Tethritercubor-turreted-tethracubor, E100#^^###>#^^###>#100
* Binet, <math>f_{\eta_{\eta_{\eta_0}}}(10)</math>
* Tristaculated-tethracubor, E100#^^###>#^^###>#^^###100
* Trinet, <math>f_{\eta_{\eta_{\eta_{\eta_0}}}}(10)</math>
* Tetrastaculated-tethracubor, E100#^^###>#^^###>#^^###>#^^###100
* Quadrinet, <math>f_{\varphi(4,0)[5]}(10)</math>
* Pentastaculated-tethracubor, E100#^^####5
* Quintinet, <math>f_{\varphi(4,0)[6]}(10)</math>
* Hexastaculated-tethracubor, E100#^^####6
* Sextinet, <math>f_{\varphi(4,0)[7]}(10)</math>
* Heptastaculated-tethracubor, E100#^^####7
* Septinet, <math>f_{\varphi(4,0)[8]}(10)</math>
* Ogdastaculated-tethracubor, E100#^^####8
* Octinet, <math>f_{\varphi(4,0)[9]}(10)</math>
* Ennastaculated-tethracubor, E100#^^####9
* Noninet / quadriphi, <math>f_{\varphi(4,0)}(10)</math>
* Dekastaculated-tethracubor, E100#^^####10
* Dekinet, <math>f_{\varphi(4,0)[11]}(10)</math>
* Icosastaculated-tethracubor, E100#^^####20
* Triantastaculated-tethracubor, E100#^^####30
* Sarantastaculated-tethracubor, E100#^^####40
* Penintastaculated-tethracubor, E100#^^####50
* Exintastaculated-tethracubor, E100#^^####60
* Ebdomintastaculated-tethracubor, E100#^^####70
* Ogdontastaculated-tethracubor, E100#^^####80
* Enenintastaculated-tethracubor, E100#^^####90
* Tethrinooteron, {100,100[1\1\1\1\2]2}
* Tethrateron / tethratesseract / tethraterror, E100#^^####100
* Hektinet, <math>f_{\varphi(4,0)[101]}(10)</math>
* Kilinet, <math>f_{\varphi(4,0)[1001]}(10)</math>
* Meginet, <math>f_{\varphi(4,0)[10^6+1]}(10)</math>
* Giginet, <math>f_{\varphi(4,0)[10^9+1]}(10)</math>
* Terinet, <math>f_{\varphi(4,0)[10^{12}+1]}(10)</math>
* Petinet, <math>f_{\varphi(4,0)[10^{15}+1]}(10)</math>
* Exinet, <math>f_{\varphi(4,0)[10^{18}+1]}(10)</math>
* Zettinet, <math>f_{\varphi(4,0)[10^{21}+1]}(10)</math>
* Yottinet, <math>f_{\varphi(4,0)[10^{24}+1]}(10)</math>

=== Part 6.7: <math>f_{\vartheta_{0}}^2(10)</math> ~ <math>f_{\varepsilon_{\vartheta_{0}+1}}^2(10)</math> ===

* Grand tethrateron, E100#^^####100#2
* Grangol-carta-tethrateron, E100#^^####100#100
* Grand grangol-carta-tethrateron, E100#^^####100#100#2
* Godgahlah-carta-tethrateron, E100#^^####100#^#100
* Godgathor-carta-tethrateron, E100#^^####100#^#^#100
* Godtothol-carta-tethrateron, E100#^^####100#^#^#^#100
* Tethrathoth-carta-tethrateron, E100#^^####100#^^#100
* Monster-Giant-carta-tethrateron, E100#^^####100(#^^#)^(#^^#)^#100
* Terrible-tethrathoth-carta-tethrateron, E100#^^####100(#^^#)^^#100
* Behemoth-Giant-carta-tethrateron, E100#^^####100(#^^#>2)^(#^^#>2)^#100
* Terrible-terrible-tethrathoth-carta-tethrateron, E100#^^####100#^^#>#3
* Trihemoth-Giant-carta-tethrateron, E100#^^####100(#^^#>3)^(#^^#>3)^#100
* Tethriterator-carta-tethrateron, E100#^^####100#^^#>#100
* Dustaculated-tethrathoth-carta-tethrateron, E100#^^####100#^^#>#^^#100
* Tethracross-carta-tethrateron, E100#^^####100#^^##100
* Tethracubor-carta-tethrateron, E100#^^####100#^^###100
* Tethrateron-by-deuteron, E100#^^####100#^^####100
* Tethrateron-by-triton, E100#^^####100#^^####100#^^####100
* Tethrateron-by-teterton, E100#^^####*#5
* Tethrateron-by-pepton, E100#^^####*#6
* Tethrateron-by-exton, E100#^^####*#7
* Tethrateron-by-epton, E100#^^####*#8
* Tethrateron-by-ogdon, E100#^^####*#9
* Tethrateron-by-enton, E100#^^####*#10
* Tethrateron-by-dekaton, E100#^^####*#11
* Tethrateron-by-hyperion, E100#^^####*#100
* Tethrateron-by-godgahlah, E100#^^####*#^#100
* Tethrateron-by-godgathor, E100#^^####*#^#^#100
* Tethrateron-by-godtothol, E100#^^####*#^#^#^#100
* Tethrateron-by-tethrathoth, E100#^^####*#^^#100
* Tethrateron-by-Monster-Giant, E100#^^####*(#^^#)^(#^^#)^#100
* Tethrateron-by-terrible-tethrathoth, E100#^^####*(#^^#)^^#100
* Tethrateron-by-Behemoth-Giant, E100#^^####*(#^^#>2)^(#^^#>2)^#100
* Tethrateron-by-terrible-terrible-tethrathoth, E100#^^####*#^^#>#3
* Tethrateron-by-Trihemoth-Giant, E100#^^####*(#^^#>3)^(#^^#>3)^#100
* Tethrateron-by-tethriterator, E100#^^####*#^^#>#100
* Tethrateron-by-dustaculated-tethrathoth, E100#^^####*#^^#>#^^#100
* Tethrateron-by-tethracross, E100#^^####*#^^##100
* Tethrateron-by-tethracubor, E100#^^####*#^^###100
* Deutero-tethrateron, E100#^^####*#^^####100
* Trito-tethrateron, E100#^^####*#^^####*#^^####100
* Teterto-tethrateron, E100(#^^####)^#4
* Pepto-tethrateron, E100(#^^####)^#5
* Exto-tethrateron, E100(#^^####)^#6
* Epto-tethrateron, E100(#^^####)^#7
* Ogdo-tethrateron, E100(#^^####)^#8
* Ento-tethrateron, E100(#^^####)^#9
* Dekato-tethrateron, E100(#^^####)^#10
* Isosto-tethrateron, E100(#^^####)^#20
* Trianto-tethrateron, E100(#^^####)^#30
* Saranto-tethrateron, E100(#^^####)^#40
* Peninto-tethrateron, E100(#^^####)^#50
* Exinto-tethrateron, E100(#^^####)^#60
* Ebdominto-tethrateron, E100(#^^####)^#70
* Ogdonto-tethrateron, E100(#^^####)^#80
* Eneninto-tethrateron, E100(#^^####)^#90
* Tethrateronifact, E100(#^^####)^#100
* Grideutertethrateron, E100(#^^####)^##100
* Kubicutethrateron, E100(#^^####)^###100
* Quarticutethrateron, E100(#^^####)^####100
* Quinticutethrateron, E100(#^^####)^#^#5
* Sexticutethrateron, E100(#^^####)^#^#6
* Septicutethrateron, E100(#^^####)^#^#7
* Octicutethrateron, E100(#^^####)^#^#8
* Nonicutethrateron, E100(#^^####)^#^#9
* Decicutethrateron, E100(#^^####)^#^#10
* Tethrateron-ad-godgahlah, E100(#^^####)^#^#100
* Tethrateron-ad-godgathor, E100(#^^####)^#^#^#100
* Tethrateron-ad-godtothol, E100(#^^####)^#^#^#^#100
* Tethrateron-ad-tethrathoth, E100(#^^####)^#^^#100
* Tethrateron-ad-Monster-Giant, E100(#^^####)^(#^^#)^(#^^#)^#100
* Tethrateron-ad-terrible-tethrathoth, E100(#^^####)^(#^^#)^^#100
* Tethrateron-ad-Behemoth-Giant, E100(#^^####)^(#^^#>2)^(#^^#>2)^#100
* Tethrateron-ad-terrible-terrible-tethrathoth, E100(#^^####)^#^^#>#3
* Tethrateron-ad-Trihemoth-Giant, E100(#^^####)^(#^^#>3)^(#^^#>3)^#100
* Tethrateron-ad-tethriterator, E100(#^^####)^#^^#>#100
* Tethrateron-ad-dustaculated-tethrathoth, E100(#^^####)^#^^#>#^^#100
* Tethrateron-ad-tethracross, E100(#^^####)^#^^##100
* Tethrateron-ad-tethracubor, E100(#^^####)^#^^###100
* Dutetrated-tethrateron, E100(#^^####)^(#^^####)100
* Tritetrated-tethrateron, E100(#^^####)^(#^^####)^(#^^####)100
* Quadratetrated-tethrateron, E100(#^^####)^^#4
* Quinquatetrated-tethrateron, E100(#^^####)^^#5
* Sexatetrated-tethrateron, E100(#^^####)^^#6
* Septatetrated-tethrateron, E100(#^^####)^^#7
* Octatetrated-tethrateron, E100(#^^####)^^#8
* Nonatetrated-tethrateron, E100(#^^####)^^#9
* Decatetrated-tethrateron, E100(#^^####)^^#10
* Terrible tethrateron, E100(#^^####)^^#100

=== Part 6.8: <math>f_{\varepsilon_{\vartheta_{0}+1}}^2(10)</math> ~ <math>f_{\Pi_{0}}^2(10)</math> ===

* Terrible terrible tethrateron, E100((#^^####)^^#)^^#100
* Three-ex-terrible tethrateron, E100(#^^####)^^#>#3
* Four-ex-terrible tethrateron, E100(#^^####)^^#>#4
* Five-ex-terrible tethrateron, E100(#^^####)^^#>#5
* Six-ex-terrible tethrateron, E100(#^^####)^^#>#6
* Seven-ex-terrible tethrateron, E100(#^^####)^^#>#7
* Eight-ex-terrible tethrateron, E100(#^^####)^^#>#8
* Nine-ex-terrible tethrateron, E100(#^^####)^^#>#9
* Ten-ex-terrible tethrateron, E100(#^^####)^^#>#10
* Territerated-tethrateron, E100(#^^####)^^#>#100
* Terriditerated-tethrateron, E100(#^^####)^^#>(#+#)100
* Territriterated-tethrateron, E100(#^^####)^^#>(#+#+#)100
* Terrigriditerated-tethrateron, E100(#^^####)^^#>##100
* Terricubiculated-tethrateron, E100(#^^####)^^#>###100
* Terriquarticulated-tethrateron, E100(#^^####)^^#>####100
* Godgahlah-turreted-territethrateron, E100(#^^####)^^#>#^#100
* Godgathor-turreted-territethrateron, E100(#^^####)^^#>#^#^#100
* Godtothol-turreted-territethrateron, E100(#^^####)^^#>#^#^#^#100
* Tethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#100
* Monster-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-territethrateron, E100(#^^####)^^#>(#^^#)^^#100
* Behemoth-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#>#3
* Trihemoth-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-territethrateron, E100(#^^####)^^#>#^^#>#100
* Dustacultethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#>#^^#100
* Tethracross-turreted-territethrateron, E100(#^^####)^^#>#^^##100
* Tethracubor-turreted-territethrateron, E100(#^^####)^^#>#^^###100
* Tethrateron-turreted-territethrateron, E100(#^^####)^^#>#^^####100
* Dustaculated-territethrateron, E100(#^^####)^^#>(#^^####)^^#100
* Tristaculated-territethrateron, E100(#^^####)^^##3
* Tetrastaculated-territethrateron, E100(#^^####)^^##4
* Pentastaculated-territethrateron, E100(#^^####)^^##5
* Hexastaculated-territethrateron, E100(#^^####)^^##6
* Heptastaculated-territethrateron, E100(#^^####)^^##7
* Octastaculated-territethrateron, E100(#^^####)^^##8
* Ennastaculated-territethrateron, E100(#^^####)^^##9
* Dekastaculated-territethrateron, E100(#^^####)^^##10
* Terrisquared-tethrateron, E100(#^^####)^^##100
* Terrible terrisquared-tethrateron, E100((#^^####)^^##)^^#100
* Dustaculated-terrible-terrisquared-tethrateron, E100((#^^####)^^##)^^#>((#^^####)^^##)^^#100
* Double terrisquared-tethrateron, E100((#^^####)^^##)^^##100
* Terrible double terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^#100
* Dustaculated-terrible-double-terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^##2
* Triple terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^##100
* Quadruple terrisquared-tethrateron, E100(#^^####)^^##>#4
* Quintuple terrisquared-tethrateron, E100(#^^####)^^##>#5
* Sextuple terrisquared-tethrateron, E100(#^^####)^^##>#6
* Septuple terrisquared-tethrateron, E100(#^^####)^^##>#7
* Octuple terrisquared-tethrateron, E100(#^^####)^^##>#8
* Nonuple terrisquared-tethrateron, E100(#^^####)^^##>#9
* Decuple terrisquared-tethrateron, E100(#^^####)^^##>#10
* Centuple terrisquared-tethrateron, E100(#^^####)^^##>#100
* Godgahlah-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#100
* Godgathor-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#^#100
* Godtothol-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#^#^#100
* Tethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#100
* Monster-Giant-turreted-terrisquared-tethrateron, E100(#^^####)^^##>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>(#^^#)^^#100
* Tethriterator-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#>#100
* Dustacultethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#>#^^#100
* Tethracross-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^##100
* Tethracubor-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^###100
* Tethrateron-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^####100
* Dustaculated-terrisquared-tethrateron, E100(#^^####)^^##>(#^^####)^^##100
* Tristaculated-terrisquared-tethrateron, E100(#^^####)^^###3
* Tetrastaculated-terrisquared-tethrateron, E100(#^^####)^^###4
* Pentastaculated-terrisquared-tethrateron, E100(#^^####)^^###5
* Hexastaculated-terrisquared-tethrateron, E100(#^^####)^^###6
* Heptastaculated-terrisquared-tethrateron, E100(#^^####)^^###7
* Octastaculated-terrisquared-tethrateron, E100(#^^####)^^###8
* Ennastaculated-terrisquared-tethrateron, E100(#^^####)^^###9
* Dekastaculated-terrisquared-tethrateron, E100(#^^####)^^###10
* Terricubed-tethrateron, E100(#^^####)^^###100
* Double terricubed-tethrateron, E100((#^^####)^^###)^^###100
* Triple terricubed-tethrateron, E100(#^^####)^^###>#3
* Quadruple terricubed-tethrateron, E100(#^^####)^^###>#4
* Quintuple terricubed-tethrateron, E100(#^^####)^^###>#5
* Sextuple terricubed-tethrateron, E100(#^^####)^^###>#6
* Septuple terricubed-tethrateron, E100(#^^####)^^###>#7
* Octuple terricubed-tethrateron, E100(#^^####)^^###>#8
* Nonuple terricubed-tethrateron, E100(#^^####)^^###>#9
* Decuple terricubed-tethrateron, E100(#^^####)^^###>#10
* Centuple terricubed-tethrateron, E100(#^^####)^^###>#100
* Godgahlah-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#100
* Godgathor-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#^#100
* Godtothol-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#^#^#100
* Tethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#100
* Monster-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#)^^#100
* Behemoth-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#3
* Trihemoth-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#100
* Dustacultethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#^^#100
* Tethracross-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^##100
* Tethracubor-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^###100
* Tethrateron-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^####100
* Dustaculated-terricubed-tethrateron, E100(#^^####)^^###>(#^^####)^^###100
* Tristaculated-terricubed-tethrateron, E100(#^^####)^^####3
* Tetrastaculated-terricubed-tethrateron, E100(#^^####)^^####4
* Pentastaculated-terricubed-tethrateron, E100(#^^####)^^####5
* Hexastaculated-terricubed-tethrateron, E100(#^^####)^^####6
* Heptastaculated-terricubed-tethrateron, E100(#^^####)^^####7
* Octastaculated-terricubed-tethrateron, E100(#^^####)^^####8
* Ennastaculated-terricubed-tethrateron, E100(#^^####)^^####9
* Dekastaculated-terricubed-tethrateron, E100(#^^####)^^####10
* Tethraduteron, E100(#^^####)^^####100
* Tethratriteron, E100((#^^####)^^####)^^####100
* Tethratetrateron, E100#^^####>#4
* Tethrapentateron, E100#^^####>#5
* Tethrahexateron, E100#^^####>#6
* Tethraheptateron, E100#^^####>#7
* Tethra-octateron, E100#^^####>#8
* Tethra-ennateron, E100#^^####>#9
* Tethradekateron, E100#^^####>#10
* Tethra-endekateron, E100#^^####>#11
* Tethradodekateron, E100#^^####>#12
* Tethra-icosateron, E100#^^####>#20
* Tethra-hectateron / tethriterteron, E100#^^####>#100
* Godgahlah-turreted-tethrateron, E100#^^####>#^#100
* Godgathor-turreted-tethrateron, E100#^^####>#^#^#100
* Godtothol-turreted-tethrateron, E100#^^####>#^#^#^#100
* Tethrathoth-turreted-tethrateron, E100#^^####>#^^#100
* Monster-Giant-turreted-tethrateron, E100#^^####>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethrateron, E100#^^####>(#^^#)^^#100
* Behemoth-Giant-turreted-tethrateron, E100#^^####>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethrateron, E100#^^####>#^^#>#3
* Trihemoth-Giant-turreted-tethrateron, E100#^^####>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethrateron, E100#^^####>#^^#>#100
* Dustacultethrathoth-turreted-tethrateron, E100#^^####>#^^#>#^^#100
* Tethracross-turreted-tethrateron, E100#^^####>#^^##100
* Tethracubor-turreted-tethrateron, E100#^^####>#^^###100
* Dustaculated-tethrateron, E100#^^####>#^^####100
* Tristaculated-tethrateron, E100#^^####>#^^####>#^^####100
* Tetrastaculated-tethrateron, E100#^^#####4
* Pentastaculated-tethrateron, E100#^^#####5
* Hexastaculated-tethrateron, E100#^^#####6
* Heptastaculated-tethrateron, E100#^^#####7
* Octastaculated-tethrateron, E100#^^#####8
* Ennastaculated-tethrateron, E100#^^#####9
* Quintiphi, <math>f_{\varphi(5,0)}(10)</math>
* Dekastaculated-tethrateron, E100#^^#####10
* Icosastaculated-tethrateron, E100#^^#####20
* Triantastaculated-tethrateron, E100#^^#####30
* Sarantastaculated-tethrateron, E100#^^#####40
* Penintastaculated-tethrateron, E100#^^#####50
* Exintastaculated-tethrateron, E100#^^#####60
* Ebdomintastaculated-tethrateron, E100#^^#####70
* Ogdontastaculated-tethrateron, E100#^^#####80
* Enenintastaculated-tethrateron, E100#^^#####90
* Tethrinoopeton, {100,100[1\1\1\1\1\2]2}
* Tethrapeton / tethrapenteract, E100#^^#^#5

=== Part 6.9: <math>f_{\Pi_{0}}^2(10)</math> ~ <math>f_{\varepsilon_{\Pi_{0}+1}}^2(10)</math> ===

* Grand tethrapeton, E100#^^#^(5)100#2
* Grangol-carta-tethrapeton, E100#^^#^(5)100#100
* Grand grangol-carta-tethrapeton, E100#^^#^(5)100#100#2
* Godgahlah-carta-tethrapeton, E100#^^#^(5)100#^#100
* Tethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#100
* Monster-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#)^(#^^#)^#100
* Territethrathoth-carta-tethrapeton, E100#^^#^(5)100(#^^#)^^#100
* Behemoth-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#>#3
* Trihemoth-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#>3)^(#^^#>3)^#100
* Tethriterator-carta-tethrapeton, E100#^^#^(5)100#^^#>#100
* Dustacultethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#>#^^#100
* Tethracross-carta-tethrapeton, E100#^^#^(5)100#^^##100
* Tethracubor-carta-tethrapeton, E100#^^#^(5)100#^^###100
* Tethrateron-carta-tethrapeton, E100#^^#^(5)100#^^####100
* Tethrapeton-by-deuteron, E100#^^#^(5)100#^^#^(5)100
* Tethrapeton-by-triton, E100#^^#^(5)100#^^#^(5)100#^^#^(5)100
* Tethrapeton-by-teterton, E100#^^#^(5)*#5
* Tethrapeton-by-pepton, E100#^^#^(5)*#6
* Tethrapeton-by-exton, E100#^^#^(5)*#7
* Tethrapeton-by-epton, E100#^^#^(5)*#8
* Tethrapeton-by-ogdon, E100#^^#^(5)*#9
* Tethrapeton-by-enton, E100#^^#^(5)*#10
* Tethrapeton-by-dekaton, E100#^^#^(5)*#11
* Tethrapeton-by-hyperion, E100#^^#^(5)*#100
* Tethrapeton-by-godgahlah, E100#^^#^(5)*#^#100
* Tethrapeton-by-tethrathoth, E100#^^#^(5)*#^^#100
* Tethrapeton-by-Monster-Giant, E100#^^#^(5)*(#^^#)^(#^^#)^#100
* Tethrapeton-by-terrible-tethrathoth, E100#^^#^(5)*(#^^#)^^#100
* Tethrapeton-by-Behemoth-Giant, E100#^^#^(5)*(#^^#>2)^(#^^#>2)^#100
* Tethrapeton-by-terrible-terrible-tethrathoth, E100#^^#^(5)*#^^#>#3
* Tethrapeton-by-Trihemoth-Giant, E100#^^#^(5)*(#^^#>3)^(#^^#>3)^#100
* Tethrapeton-by-tethriterator, E100#^^#^(5)*#^^#>#100
* Tethrapeton-by-dustaculated-tethrathoth, E100#^^#^(5)*#^^#>#^^#100
* Tethrapeton-by-tethracross, E100#^^#^(5)*#^^##100
* Tethrapeton-by-tethracubor, E100#^^#^(5)*#^^###100
* Tethrapeton-by-tethrateron, E100#^^#^(5)*#^^####100
* Deutero-tethrapeton, E100#^^#^(5)*#^^#^(5)100
* Trito-tethrapeton, E100#^^#^(5)*#^^#^(5)*#^^#^(5)100
* Teterto-tethrapeton, E100(#^^#^5)^#4
* Pepto-tethrapeton, E100(#^^#^5)^#5
* Exto-tethrapeton, E100(#^^#^5)^#6
* Epto-tethrapeton, E100(#^^#^5)^#7
* Ogdo-tethrapeton, E100(#^^#^5)^#8
* Ento-tethrapeton, E100(#^^#^5)^#9
* Dekato-tethrapeton, E100(#^^#^5)^#10
* Isosto-tethrapeton, E100(#^^#^5)^#20
* Trianto-tethrapeton, E100(#^^#^5)^#30
* Saranto-tethrapeton, E100(#^^#^5)^#40
* Peninto-tethrapeton, E100(#^^#^5)^#50
* Exinto-tethrapeton, E100(#^^#^5)^#60
* Ebdominto-tethrapeton, E100(#^^#^5)^#70
* Ogdonto-tethrapeton, E100(#^^#^5)^#80
* Eneninto-tethrapeton, E100(#^^#^5)^#90
* Tethrapetonifact, E100(#^^#^5)^#100
* Quadratatethrapeton, E100(#^^#^5)^##100
* Kubikutethrapeton, E100(#^^#^5)^###100
* Quarticutethrapeton, E100(#^^#^5)^####100
* Quinticutethrapeton, E100(#^^#^5)^#^#5
* Sexticutethrapeton, E100(#^^#^5)^#^#6
* Septicutethrapeton, E100(#^^#^5)^#^#7
* Octicutethrapeton, E100(#^^#^5)^#^#8
* Nonicutethrapeton, E100(#^^#^5)^#^#9
* Decicutethrapeton, E100(#^^#^5)^#^#10
* Tethrapeton-ipso-godgahlah, E100(#^^#^5)^#^#100
* Tethrapeton-ipso-tethrathoth, E100(#^^#^5)^#^^#100
* Tethrapeton-ipso-Monster-Giant, E100(#^^#^5)^(#^^#)^(#^^#)^#100
* Tethrapeton-ipso-terrible-tethrathoth, E100(#^^#^5)^(#^^#)^^#100
* Tethrapeton-ipso-Behemoth-Giant, E100(#^^#^5)^(#^^#>2)^(#^^#>2)^#100
* Tethrapeton-ipso-terrible-terrible-tethrathoth, E100(#^^#^5)^#^^#>#3
* Tethrapeton-ipso-Trihemoth-Giant, E100(#^^#^5)^(#^^#>3)^(#^^#>3)^#100
* Tethrapeton-ipso-tethriterator, E100(#^^#^5)^#^^#>#100
* Tethrapeton-ipso-dustaculated-tethrathoth, E100(#^^#^5)^#^^#>#^^#100
* Tethrapeton-ipso-tethracross, E100(#^^#^5)^#^^##100
* Tethrapeton-ipso-tethracubor, E100(#^^#^5)^#^^###100
* Tethrapeton-ipso-tethrateron, E100(#^^#^5)^#^^####100
* Dutetrated-tethrapeton, E100(#^^#^5)^(#^^#^5)100
* Tritetrated-tethrapeton, E100(#^^#^5)^(#^^#^5)^(#^^#^5)100
* Quadratetrated-tethrapeton, E100(#^^#^5)^^#4
* Quintatetrated-tethrapeton, E100(#^^#^5)^^#5
* Sexatetrated-tethrapeton, E100(#^^#^5)^^#6
* Septatetrated-tethrapeton, E100(#^^#^5)^^#7
* Octatetrated-tethrapeton, E100(#^^#^5)^^#8
* Nonatetrated-tethrapeton, E100(#^^#^5)^^#9
* Decatetrated-tethrapeton, E100(#^^#^5)^^#10
* Terrible tethrapeton, E100(#^^#^5)^^#100

=== Part 6.10: <math>f_{\varepsilon_{\Pi_{0}+1}}^2(10)</math> ~ <math>f_{\varpi_{0}}^2(10)</math> ===

* Terrible terrible tethrapeton, E100((#^^#^5)^^#)^^#100
* Three-ex-terrible tethrapeton, E100(#^^#^5)^^#>#3
* Four-ex-terrible tethrapeton, E100(#^^#^5)^^#>#4
* Five-ex-terrible tethrapeton, E100(#^^#^5)^^#>#5
* Six-ex-terrible tethrapeton, E100(#^^#^5)^^#>#6
* Seven-ex-terrible tethrapeton, E100(#^^#^5)^^#>#7
* Eight-ex-terrible tethrapeton, E100(#^^#^5)^^#>#8
* Nine-ex-terrible tethrapeton, E100(#^^#^5)^^#>#9
* Ten-ex-terrible tethrapeton, E100(#^^#^5)^^#>#10
* Territerated tethrapeton, E100(#^^#^5)^^#>#100
* Dustaculated-territethrapeton, E100(#^^#^5)^^#>(#^^#^5)^^#100
* Terrisquared-tethrapeton, E100(#^^#^5)^^##100
* Two-ex-terrisquared-tethrapeton, E100((#^^#^5)^^##)^^##100
* Three-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#3
* Four-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#4
* Five-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#5
* Six-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#6
* Seven-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#7
* Eight-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#8
* Nine-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#9
* Ten-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#10
* Tethritercrossed-tethrapeton, E100(#^^#^5)^^##>#100
* Dustaculated-terrisquared-tethrapeton, E100(#^^#^5)^^##>(#^^#^5)^^##100
* Terricubed-tethrapeton, E100(#^^#^5)^^###100
* Two-ex-terricubed-tethrapeton, E100((#^^#^5)^^###)^^###100
* Three-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#3
* Four-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#4
* Five-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#5
* Six-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#6
* Seven-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#7
* Eight-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#8
* Nine-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#9
* Ten-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#10
* Tethritercubed-tethrapeton, E100(#^^#^5)^^###>#100
* Dustaculated-terricubed-tethrapeton, E100(#^^#^5)^^###>(#^^#^5)^^###100
* Territesserated-tethrapeton, E100(#^^#^5)^^####100
* Two-ex-territesserated-tethrapeton, E100((#^^#^5)^^####)^^####100
* Three-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#3
* Four-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#4
* Five-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#5
* Six-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#6
* Seven-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#7
* Eight-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#8
* Nine-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#9
* Ten-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#10
* Tethritertesserated-tethrapeton, E100(#^^#^5)^^####>#100
* Dustaculated-territesserated-tethrapeton, E100(#^^#^5)^^####>(#^^#^5)^^####100
* Tethradupeton, E100(#^^#^5)^^#^(5)100
* Tethratripeton, E100((#^^#^5)^^#^5)^^#^(5)100
* Tethratetrapeton, E100(((#^^#^5)^^#^5)^^#^5)^^#^(5)100
* Tethrapentapeton, E100#^^(#^5)>#5
* Tethrahexapeton, E100#^^(#^5)>#6
* Tethraheptapeton, E100#^^(#^5)>#7
* Tethra-octapeton, E100#^^(#^5)>#8
* Tethra-ennapeton, E100#^^(#^5)>#9
* Tethradekapeton, E100#^^(#^5)>#10
* Tethra-endekapeton, E100#^^(#^5)>#11
* Tethradodekapeton, E100#^^(#^5)>#12
* Tethra-icosapeton, E100#^^(#^5)>#20
* Tethriterpeton, E100#^^(#^5)>#100
* Godgahlah-turreted-tethrapeton, E100#^^(#^5)>#^#100
* Tethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#100
* Monster-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethrapeton, E100#^^(#^5)>(#^^#)^^#100
* Behemoth-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#>#3
* Trihemoth-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethrapeton, E100#^^(#^5)>#^^#>#100
* Dustacultethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#>#^^#100
* Tethracross-turreted-tethrapeton, E100#^^(#^5)>#^^##100
* Tethracubor-turreted-tethrapeton, E100#^^(#^5)>#^^###100
* Tethrateron-turreted-tethrapeton, E100#^^(#^5)>#^^####100
* Dustaculated-tethrapeton, E100#^^(#^5)>#^^#^(5)100
* Tristaculated-tethrapeton, E100#^^(#^5)>#^^(#^5)>#^^#^(5)100
* Tetrastaculated-tethrapeton, E100#^^(#^5)>#^^(#^5)>#^^(#^5)>#^^#^(5)100
* Pentastaculated-tethrapeton, E100#^^#^(6)5
* Hexastaculated-tethrapeton, E100#^^#^(6)6
* Heptastaculated-tethrapeton, E100#^^#^(6)7
* Octastaculated-tethrapeton, E100#^^#^(6)8
* Ennastaculated-tethrapeton, E100#^^#^(6)9
* Sextiphi, <math>f_{\varphi(6,0)}(10)</math>
* Dekastaculated-tethrapeton, E100#^^#^(6)10
* Icosastaculated-tethrapeton, E100#^^#^(6)20
* Triantastaculated-tethrapeton, E100#^^#^(6)30
* Sarantastaculated-tethrapeton, E100#^^#^(6)40
* Penintastaculated-tethrapeton, E100#^^#^(6)50
* Exintastaculated-tethrapeton, E100#^^#^(6)60
* Ebdomintastaculated-tethrapeton, E100#^^#^(6)70
* Ogdontastaculated-tethrapeton, E100#^^#^(6)80
* Enenintastaculated-tethrapeton, E100#^^#^(6)90
* Tethrinoohexon, {100,100[1\1\1\1\1\1\2]2}
* Tethrahexon / tethrahexeract, E100#^^#^#6

=== Part 6.11: <math>f_{\varpi_{0}}^2(10)</math> ~ <math>f_{\varphi(\omega,0)}^2(10)</math> ===

* Grand tethrahexon, E100#^^#^(6)100#2
* Grangol-carta-tethrahexon, E100#^^#^(6)100#100
* Grand grangol-carta-tethrahexon, E100#^^#^(6)100#100#2
* Godgahlah-carta-tethrahexon, E100#^^#^(6)100#^#100
* Tethrathoth-carta-tethrahexon, E100#^^#^(6)100#^^#100
* Tethracross-carta-tethrahexon, E100#^^#^(6)100#^^##100
* Tethracubor-carta-tethrahexon, E100#^^#^(6)100#^^###100
* Tethrateron-carta-tethrahexon, E100#^^#^(6)100#^^####100
* Tethrapeton-carta-tethrahexon, E100#^^#^(6)100#^^#^(5)100
* Tethrahexon-by-deuteron, E100#^^#^(6)100#^^#^(6)100
* Tethrahexon-by-triton, E100#^^#^(6)100#^^#^(6)100#^^#^(6)100
* Tethrahexon-by-teterton, E100(#^^#^6)*#5
* Tethrahexon-by-pepton, E100(#^^#^6)*#6
* Tethrahexon-by-exton, E100(#^^#^6)*#7
* Tethrahexon-by-epton, E100(#^^#^6)*#8
* Tethrahexon-by-ogdon, E100(#^^#^6)*#9
* Tethrahexon-by-enton, E100(#^^#^6)*#10
* Tethrahexon-by-dekaton, E100(#^^#^6)*#11
* Tethrahexon-by-hyperion, E100(#^^#^6)*#100
* Tethrahexon-by-godgahlah, E100(#^^#^6)*#^#100
* Tethrahexon-by-tethrathoth, E100(#^^#^6)*#^^#100
* Tethrahexon-by-tethracross, E100(#^^#^6)*#^^##100
* Tethrahexon-by-tethracubor, E100(#^^#^6)*#^^###100
* Tethrahexon-by-tethrateron, E100(#^^#^6)*#^^####100
* Tethrahexon-by-tethrapeton, E100(#^^#^6)*(#^^#^5)100
* Deutero-tethrahexon, E100#^^#^(6)*#^^#^(6)100
* Trito-tethrahexon, E100#^^#^(6)*#^^#^(6)*#^^#^(6)100
* Teterto-tethrahexon, E100#^^#^(6)*#^^#^(6)*#^^#^(6)*#^^#^(6)100
* Pepto-tethrahexon, E100(#^^#^6)^#5
* Exto-tethrahexon, E100(#^^#^6)^#6
* Epto-tethrahexon, E100(#^^#^6)^#7
* Ogdo-tethrahexon, E100(#^^#^6)^#8
* Ento-tethrahexon, E100(#^^#^6)^#9
* Dekato-tethrahexon, E100(#^^#^6)^#10
* Tethrahexonifact, E100(#^^#^6)^#100
* Quadratatethrahexon, E100(#^^#^6)^##100
* Kubikutethrahexon, E100(#^^#^6)^###100
* Quarticutethrahexon, E100(#^^#^6)^####100
* Quinticutethrahexon, E100(#^^#^6)^#^#5
* Sexticutethrahexon, E100(#^^#^6)^#^#6
* Septicutethrahexon, E100(#^^#^6)^#^#7
* Octicutethrahexon, E100(#^^#^6)^#^#8
* Nonicutethrahexon, E100(#^^#^6)^#^#9
* Decicutethrahexon, E100(#^^#^6)^#^#10
* Tethrahexon-ipso-godgahlah, E100(#^^#^6)^#^#100
* Tethrahexon-ipso-godgathor, E100(#^^#^6)^#^#^#100
* Tethrahexon-ipso-godtothol, E100(#^^#^6)^#^#^#^#100
* Tethrahexon-ipso-tethrathoth, E100(#^^#^6)^#^^#100
* Tethrahexon-ipso-tethracross, E100(#^^#^6)^#^^##100
* Tethrahexon-ipso-tethracubor, E100(#^^#^6)^#^^###100
* Tethrahexon-ipso-tethrateron, E100(#^^#^6)^#^^####100
* Tethrahexon-ipso-tethrapeton, E100(#^^#^6)^(#^^#^5)100
* Dutetrated-tethrahexon, E100(#^^#^6)^(#^^#^6)100
* Tritetrated-tethrahexon, E100(#^^#^6)^(#^^#^6)^(#^^#^6)100
* Quadratetrated-tethrahexon, E100(#^^#^6)^^#4
* Quinquatetrated-tethrahexon, E100(#^^#^6)^^#5
* Sexatetrated-tethrahexon, E100(#^^#^6)^^#6
* Septatetrated-tethrahexon, E100(#^^#^6)^^#7
* Octatetrated-tethrahexon, E100(#^^#^6)^^#8
* Nonatetrated-tethrahexon, E100(#^^#^6)^^#9
* Decatetrated-tethrahexon, E100(#^^#^6)^^#10
* Terrible tethrahexon, E100(#^^#^6)^^#100
* Terrible terrible tethrahexon, E100((#^^#^6)^^#)^^#100
* Three-ex-terrible tethrahexon, E100(#^^#^6)^^#>#3
* Four-ex-terrible tethrahexon, E100(#^^#^6)^^#>#4
* Territerated tethrahexon, E100(#^^#^6)^^#>#100
* Dustaculated-territethrahexon, E100(#^^#^6)^^#>(#^^#^6)^^#100
* Terrisquared-tethrahexon, E100(#^^#^6)^^##100
* Dustaculated-terrisquared-tethrahexon, E100(#^^#^6)^^##>(#^^#^6)^^##100
* Ennastaculated-terrisquared-tethrahexon, E100(#^^#^6)^^###9
* Ennastaculated-terricubed-tethrahexon, E100(#^^#^6)^^####9
* Ennastaculated-territesserated-tethrahexon, E100((#^^#^6)^^#^5)9
* Dustaculated-tethrahexon / tethrahexon-turreted-tethrahexon, E100#^^(#^6)>#^^(#^6)100
* Septiphi, <math>f_{\varphi(7,0)}(10)</math>
* Dekastaculated-tethrahexon, E100#^^(#^7)10
* Tethrinoohepton, {100,100[1\1\1\1\1\1\1\2]2}
* Tethrahepton, E100#^^#^#7
* Grand tethrahepton, E100#^^#^(7)100#2
* Grangol-carta-tethrahepton, E100#^^#^(7)100#100
* Tethrahepton-by-deuteron, E100#^^#^(7)100#^^#^(7)100
* Tethrahepton-by-hyperion, E100(#^^#^7)*#100
* Deutero-tethrahepton, E100#^^#^(7)*#^^#^(7)100
* Trito-tethrahepton, E100#^^#^(7)*#^^#^(7)*#^^#^(7)100
* Teterto-tethrahepton, E100(#^^#^7)^#4
* Pepto-tethrahepton, E100(#^^#^7)^#5
* Ogdo-tethrahepton, E100(#^^#^7)^#8
* Ento-tethrahepton, E100(#^^#^7)^#9
* Tethraheptonifact, E100(#^^#^7)^#100
* Terrible tethrahepton, E100(#^^#^7)^^#100
* Octiphi, <math>f_{\varphi(8,0)}(10)</math>
* Dekastaculated-tethrahepton, E100#^^(#^8)10
* Tethrinoo-ogdon, {100,100[1\1\1\1\1\1\1\1\2]2}
* Tethra-ogdon, E100#^^#^#8
* Deutero-tethra-ogdon, E100#^^#^(8)*#^^#^(8)100
* Trito-tethra-ogdon, E100#^^#^(8)*#^^#^(8)*#^^#^(8)100
* Teterto-tethra-ogdon, E100#^^#^(8)*#^^#^(8)*#^^#^(8)*#^^#^(8)100
* Ogdo-tethra-ogdon, E100(#^^#^8)^#8
* Noniphi, <math>f_{\varphi(9,0)}(10)</math>
* Tethrinoo-ennon, {100,100[1\1\1\1\1\1\1\1\1\2]2}
* Tethrennon, E100#^^#^#9
* Grand tethrennon, E100#^^#^(9)100#2
* Grangol-carta-tethrennon, E100#^^#^(9)100#100
* Tethrennon-by-deuteron, E100#^^#^(9)100#^^#^(9)100
* Deutero-tethrennon, E100#^^#^(9)*#^^#^(9)100
* Teterto-tethrennon, E100#^^#^(9)*#^^#^(9)*#^^#^(9)*#^^#^(9)100
* Tethrennonifact, E100(#^^#^9)^#100
* Dutetrated-tethrennon, E100(#^^#^9)^(#^^#^9)100
* Terrible tethrennon, E100(#^^#^9)^^#100
* Territerated tethrennon, E100(#^^#^9)^^#>#100
* Dustaculated-territethrennon, E100(#^^#^9)^^#>(#^^#^9)^^#100
* Terrisquared-tethrennon, E100(#^^#^9)^^##100
* Terricubed-tethrennon, E100(#^^#^9)^^###100
* Territesserated-tethrennon, E100(#^^#^9)^^####100
* Terripenterated-tethrennon, E100(#^^#^9)^^#####100
* Terrihexerated-tethrennon, E100(#^^#^9)^^######100
* Terrihepterated-tethrennon, E100(#^^#^9)^^#######100
* Terriocterated-tethrennon, E100(#^^#^9)^^########100
* Two-ex-terriocterated-tethrennon, E100((#^^#^9)^^#^8)^^#^(8)100
* Tethradu-ennon, E100(#^^#^9)^^#^(9)100
* Dekophi / omphi, <math>f_{\varphi(10,0)}(10)=f_{\varphi(\omega,0)}(10)</math>
* Tethrinoodekon, {100,100[1\1\1\1\1\1\1\1\1\1\2]2}
* Tethradekon, E100#^^#^#10
* Grand tethradekon, E100#^^#^(10)100#2
* Deutero-tethradekon, E100#^^#^(10)*#^^#^(10)100
* Teterto-tethradekon, E100#^^#^(10)*#^^#^(10)*#^^#^(10)*#^^#^(10)100
* Tethrinoo-icoson, {100,20[1[2¬2]2]2}
* Tethrinootope, {100,100[1[2¬2]2]2}
* Hektophi, <math>f_{\varphi(100,0)}(10)</math>
* ''Goppatope'', 100^^100100&10
* Tethratope / tethrahecton / tethratopos, E100#^^#^#100
* Deutero-tethrahecton, E100#^^#^(100)*#^^#^(100)100
* Humonurgium, <math>f_{\varphi(\omega,0)}(420)</math>
* Kilophi, <math>f_{\varphi(1000,0)}(10)</math>
* Tethrachillion, E100#^^#^#1000
* Tethramyrion, E100#^^#^#10000
* Megophi, <math>f_{\varphi(10^6,0)}(10)</math>
* Gigophi, <math>f_{\varphi(10^9,0)}(10)</math>
* Terophi, <math>f_{\varphi(10^{12},0)}(10)</math>
* Petophi, <math>f_{\varphi(10^{15},0)}(10)</math>
* Exophi, <math>f_{\varphi(10^{18},0)}(10)</math>
* Zettophi, <math>f_{\varphi(10^{21},0)}(10)</math>
* Yottophi, <math>f_{\varphi(10^{24},0)}(10)</math>

=== Part 6.12: <math>f_{\varphi(\omega,0)}^2(10)</math> ~ <math>f_{\Gamma_0}^2(10)</math> ===

* Grand tethratope, E100#^^#^#100#2
* Grangol-carta-tethratope, E100#^^#^#100#100
* Greagol-carta-tethratope, E100#^^#^#100#100#100
* Gugold-carta-tethratope, E100#^^#^#100##100
* Throogol-carta-tethratope, E100#^^#^#100###100
* Tetroogol-carta-tethratope, E100#^^#^#100####100
* Godgahlah-carta-tethratope, E100#^^#^#100#^#100
* Godgathor-carta-tethratope, E100#^^#^#100#^#^#100
* Godtothol-carta-tethratope, E100#^^#^#100#^#^#^#100
* Tethrathoth-carta-tethratope, E100#^^#^#100#^^#100
* Monster-Giant-carta-tethratope, E100#^^#^#100(#^^#)^(#^^#)^#100
* Tethracross-carta-tethratope, E100#^^#^#100#^^##100
* Tethracubor-carta-tethratope, E100#^^#^#100#^^###100
* Tethrateron-carta-tethratope, E100#^^#^#100#^^####100
* Tethratope-by-deuteron / tethratope-carta-tethratope, E100#^^#^#100#^^#^#100
* Tethratope-by-triton, E100#^^#^#100#^^#^#100#^^#^#100
* Tethratope-by-hyperion, E100#^^#^#*#100
* Deutero-tethratope, E100#^^#^#*#^^#^#100
* Hecato-tethratope / tethratopofact, E100(#^^#^#)^#100
* Terrible tethratope, E100(#^^#^#)^^#100
* Territertethratope / tethriterated-tethratope, E100(#^^#^#)^^#>#100
* Dustaculated-territethratope, E100(#^^#^#)^^#>(#^^#^#)^^#100
* Terrisquared tethratope, E100(#^^#^#)^^##100
* Terricubed tethratope, E100(#^^#^#)^^###100
* Territesserated tethratope, E100(#^^#^#)^^####100
* Tethradeutertope, E100(#^^#^#)^^#^#100
* Tethratritotope, E100((#^^#^#)^^#^#)^^#^#100
* Tethritertope, E100#^^(#^#)>#100
* Dustaculated-tethratope, E100#^^(#^#)>#^^(#^#)100
* Tethratopothoth, E100#^^(#^#*#)100
* Dustaculated-tethratopothoth, E100#^^(#^#*#)>#^^(#^#*#)100
* Tethratopocross, E100#^^(#^#*##)100
* Tethratopocubor, E100#^^(#^#*###)100
* Tethratopoteron, E100#^^(#^#*####)100
* Tethratopopeton, E100#^^(#^#*#####)100
* Tethratopodeus, E100#^^(#^#*#^#)100
* Tethratopodeusithoth, E100#^^(#^#*#^#*#)100
* Tethratopodeusicross, E100#^^(#^#*#^#*##)100
* Tethratopotruce, E100#^^(#^#*#^#*#^#)100
* Tethratopoquad, E100#^^(#^#*#^#*#^#*#^#)100
* Tethratopoquid, E100#^^(#^#*#^#*#^#*#^#*#^#)100
* Tethratoposid, E100#^^#^##6
* Tethrinoolattitope, {100,100[1[3¬2]2]2}
* Tethralattitope, E100#^^#^##100
* Even More Godder Tritri, 3 [3 {3 /// 3} 3] 3
* Tethralattitopothoth, E100#^^(#^##*#)100
* Tethralattitopotope, E100#^^(#^##*#^#)100
* Tethralattitopodeus, E100#^^(#^##*#^##)100
* ''Triakulus'', 3^^^3 & 3
* Tethralattitopotruce, E100#^^(#^##*#^##*#^##)100
* Tethralattitopoquad, E100#^^(#^##*#^##*#^##*#^##)100
* Tethracubitope, E100#^^#^###100
* Tethrinooquartitope, {100,100[1[5¬2]2]2}
* Tethraquarticutope, E100#^^#^####100
* Tethraquinticutope, E100#^^#^#####100
* Tethrasexticutope, E100#^^#^######100
* Tethrasepticutope, E100#^^#^#^(7)100
* Tethra-octicutope, E100#^^#^#^(8)100
* Tethrinooquartitope, {100,100[1[5¬2]2]2}
* Tethrinoononitope, {100,100[1[10¬2]2]2}
* Tethranonicutope, E100#^^#^#^(9)100
* Tethradecicutope, E100#^^#^#^(10)100
* Tethradecicutopononicutopo-octicutoposepticutoposexticutopoquinticutopoquarticutopocubitopolattitopotope, E100#^^(#^##########*#^#########*#^########*#^#######*#^######*#^#####*#^####*#^###*#^##*#^#)100
* Juice infused DLMAN, 17[1 {186 (/44) 416} 2]592 = 17[1 {196 `44` 416} 2]592
* Tethrato-godgathor / tethraspatialtope, E100#^^#^#^#100
* Tethrato-gotrigathor / dustaculated-tethraspatialtope, E100#^^(#^#^#)>#^^#^#^#100
* Tethrato-godgoldgathor, E100#^^(#^#^#*#)100
* Tethrato-godthroogathor, E100#^^(#^#^#*##)100
* Tethrato-godgathor-by-godgahlah-propinquus, E100#^^(#^#^#*#^#)100
* Tethrato-godgathor-by-gridgahlah-propinquus, E100#^^(#^#^#*#^##)100
* Tethrato-deutero-godgathor / tethraspatialtopodeus, E100#^^(#^#^#*#^#^#)100
* Tethrato-trito-godgathor / tethraspatialtopotruce, E100#^^(#^#^#*#^#^#*#^#^#)100
* Tethrato-godgathorfact / tethraspatialtopocentice, E100#^^#^(#^#*#)100
* Tethrato-deutero-godgathorfact, E100#^^(#^(#^#*#)*#^(#^#*#))100
* Tethrato-godgridgathor, E100#^^#^(#^#*##)100
* Tethrato-godkubikgathor, E100#^^#^(#^#*###)100
* Tethrato-godquarticgathor, E100#^^#^(#^#*####)100
* Tethrato-godgathordeus, E100#^^#^(#^#*#^#)100
* Tethrato-godgathordeucifact, E100#^^#^(#^#*#^#*#)100
* Tethrato-godgathortruce, E100#^^#^(#^#*#^#*#^#)100
* Tethrato-godgathorquad, E100#^^#^(#^#*#^#*#^#*#^#)100
* Tethrato-gralgathor, E100#^^#^#^##100
* Tethrato-godtothol, E100#^^#^#^#^#100
* Tethrato-godtertol, E100#^^#^^#5
* Tethrato-godtopol, E100#^^#^^#6
* Tethrato-godhathor, E100#^^#^^#7
* Tethrato-godheptol, E100#^^#^^#8
* Binphi, <math>f_{\varphi(\varphi(1,0),0)}(10)</math>
* Tethrinoogarxitri, {100,100[1[1[1\2]2¬2]2]2}
* '''Tethrato-tethrathoth''' / tethrarxitri, E100#^^#^^#100
* Hectastaculated-tethrato-tethrathoth / tethrato-tethrathoth-by-hyperion-propinquus, E100#^^(#^^#*#)100
* Tethrato-tethrathoth-by-godgahlah-propinquus, E100#^^(#^^#*#^#)100
* Tethrato-deutero-tethrathoth, E100#^^(#^^#*#^^#)100
* Tethrato-tethrafact, E100#^^(#^^#)^#100
* Tethrato-tethraduliath, E100#^^(#^^#)^(#^^#)100
* Tethrato-Monster-Giant, E100#^^(#^^#)^(#^^#)^#100
* Tethrato-tethrathoth-trebletetrate, E100#^^(#^^#)^(#^^#)^(#^^#)100
* Tethrato-Super-Monster-Giant, E100#^^(#^^#)^(#^^#)^(#^^#)^#100
* Tethrato-terrible-tethrathoth, E100#^^(#^^#)^^#100
* Tethrato-tethriterator, E100#^^(#^^#>#)100
* Tethrato-dustaculated-tethrathoth, E100#^^(#^^#>#^^#)100
* Tethrato-tethracross, E100#^^#^^##100
* Tethrato-tethracubor, E100#^^#^^###100
* Tethrato-tethratope, E100#^^#^^#^#100
* Brother-Giant / Cintaur, E100#^^#^#^^#^#100
* Tethrato-tethralattitope, E100#^^#^^#^##100
* Tethrato-tethraspatialtope / dutethrato-godgathor, E100#^^#^^#^#^#100
* Dutethrato-godtothol, E100#^^#^^#^#^#^#100
* Trinphi, <math>f_{\varphi(\varphi(\varphi(1,0),0),0)}(10)</math>
* Tethrinoogarxitet, {100,100[1[1[1[1[1\2]2¬2]2]2¬2]2]2}
* Tethrarxitet / tethrato-tethrato-tethrathoth, E100#^^#^^#^^#100
* Tethrato-tethrarxitri-by-gugold-propinquus, E100#^^(#^^#^^#*#)100
* Tethrato-deutero-tethrarxitri, E100#^^(#^^#^^#*#^^#^^#)100
* Tethrato-dustaculated-tethrarxitri, E100#^^(#^^(#^^#)>#^^#^^#)100
* Dutethrato-tethrathoth-by-gugold-propinquus, E100#^^#^^(#^^#*#)100
* Dutethrato-tethriterator, E100#^^#^^#^^#>#100
* Dutethrato-tethracross, E100#^^#^^#^^##100
* Dutethrato-tethratope, E100#^^#^^#^^#^#100
* Quadrinphi, <math>f_{\varphi(\varphi(\varphi(\varphi(1,0),0),0),0)}(10)</math>
* Tethrinoogarxipent, {100,100[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxipent, E100#^^#^^#^^#^^#100
* Quintinphi, <math>f_{\Gamma_0[6]}(10)</math>
* Tethrinoogarxihex, {100,100[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxihex, E100#^^^#6
* Sextinphi, <math>f_{\Gamma_0[7]}(10)</math>
* Tethrinoogarxihept, {100,100[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxihept, E100#^^^#7
* Septinphi, <math>f_{\Gamma_0[8]}(10)</math>
* Tethrinoogarxiogd, {100,100[1[1[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxi-ogd, E100#^^^#8
* Octinphi, <math>f_{\Gamma_0[9]}(10)</math>
* Tethrinoogarxienn, {100,100[1[1[1[1[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxi-enn, E100#^^^#9
* Noninphi / Unexommthet, <math>f_{\Gamma_0}(10)</math>
* Pentabackthulhum, {10,10[1[1\2¬2]2]2}
* Tethrinoogarxideck, {100,10[1[1\2¬2]2]2}
* Tethrarxideck, E100#^^^#10
* Dekinphi, <math>f_{\Gamma_0[11]}(10)</math>
* Tethrinoogarxicose, {100,20[1[1\2¬2]2]2}
* Tethrarxicose, E100#^^^#20
* Tethrinoogarxitriane, {100,30[1[1\2¬2]2]2}
* Tethrarxitriane, E100#^^^#30
* Tethrinoogarxisarane, {100,40[1[1\2¬2]2]2}
* Tethrarxisarane, E100#^^^#40
* Tethrinoogarxipenine, {100,50[1[1\2¬2]2]2}
* Tethrarxipenine / tethrarxigole, E100#^^^#50
* Tethrinoogarxiexine, {100,60[1[1\2¬2]2]2}
* Tethrarxi-exine, E100#^^^#60
* Tethrinoogarxiebdomine, {100,70[1[1\2¬2]2]2}
* Tethrarxi-ebdomine, E100#^^^#70
* Tethrinoogarxiogdone, {100,80[1[1\2¬2]2]2}
* Tethrarxi-ogdone, E100#^^^#80
* Tethrinoogarxienenine, {100,90[1[1\2¬2]2]2}
* Tethrarxi-enenine, E100#^^^#90
* Pentacthuloogol / tethrinoogarxihect, {100,100[1[1\2¬2]2]2}
* Pentacthulhum / tethrarxihect, E100#^^^#100
* ''Kungulus'', <math>X \uparrow \uparrow \uparrow 100 \& 10</math>
* ''Second Kungulus'', {100,100,3} & 10
* Onii-chan-Giant, E100#^^#^#^^#^#^^#^ ... #^^#^#100 (100 #^^#'s)
* Hektinphi, <math>f_{\Gamma_0[101]}(10)</math>
* Tethrinoogarxigigas, {100,500[1[1\2¬2]2]2}
* Tethrarxigigas, E100#^^^#500
* Mariupol, <math>f_{\Gamma_0}(576)</math>
* Tethrinoogarxichill, {100,1000[1[1\2¬2]2]2}
* Tethrarxichill, E100#^^^#1,000
* Kilinphi, <math>f_{\Gamma_0[1001]}(10)</math>
* Tethrinoogarximyr, {100,10000[1[1\2¬2]2]2}
* Tethrarximyr, E100#^^^#10,000
* Tethrarxigong, E100#^^^#100,000
* Pentacthulhugong, E100,000#^^^#100,000
* Meginphi, <math>f_{\Gamma_0[10^6+1]}(10)</math>
* Tethrinoogarxi-octad, {100,{10,8}[1[1\2¬2]2]2}
* Tethrarxi-octad, E100#^^^#100,000,000
* Giginphi, <math>f_{\Gamma_0[10^9+1]}(10)</math>
* Great Wall, E100#^^#^^#>#^^#^^#>#^^#^^#>...#^^#^^#>#^^#^^#100 (with 10,000,000,000 #^^#^^#'s)
* Terinphi, <math>f_{\Gamma_0[10^{12}+1]}(10)</math>
* Petinphi, <math>f_{\Gamma_0[10^{15}+1]}(10)</math>
* Tethrinoogarxi-sedeniad], {100,{10,16}[1[1\2¬2]2]2}
* Tethrarxi-sedeniad, E100#^^^#10,000,000,000,000,000
* Exinphi, <math>f_{\Gamma_0[10^{18}+1]}(10)</math>
* Zettinphi, <math>f_{\Gamma_0[10^{21}+1]}(10)</math>
* Yottinphi, <math>f_{\Gamma_0[10^{24}+1]}(10)</math>
* Tethrarxigoogliad, E100#^^^#(10100)
* Tethrarxigrangliad, E100#^^^#(E100#100)

== Bachmann's collapsing level ==

=== Part 6.13: <math>f_{\Gamma_0}^2(10)</math> ~ <math>f_{\Gamma_1}^2(10)</math> ===

* Grand pentacthulhum / grand tethrarxihect / tethrarxitethrarxihect, E100#^^^#100#2
* Grand grand pentacthulhum, E100#^^^#100#3
* Triple grand pentacthulhum, E100#^^^#100#4
* Quadruple grand pentacthulhum, E100#^^^#100#5
* Quintuple grand pentacthulhum, E100#^^^#100#6
* Sextuple grand pentacthulhum, E100#^^^#100#7
* Septuple grand pentacthulhum, E100#^^^#100#8
* Octuple grand pentacthulhum, E100#^^^#100#9
* Nonuple grand pentacthulhum, E100#^^^#100#10
* Decuple grand pentacthulhum, E100#^^^#100#11
* Grangol-carta-pentacthulhum, E100#^^^#100#100
* Greagol-carta-pentacthulhum, E100#^^^#100#100#100
* Gigangol-carta-pentacthulhum, E100#^^^#100#100#100#100
* Gugold-carta-pentacthulhum, E100#^^^#100##100
* Gammaxul, <math>200![200(1)2]</math>
* Throogol-carta-pentacthulhum, E100#^^^#100###100
* Tethratope-carta-pentacthulhum, E100#^^^#100#^^#^#100
* Tethrarxitri-carta-pentacthulhum, E100#^^^#100#^^#^^#100
* Pentacthulhutri, E100#^^^#100#^^^#100
* Pentacthulhutet, E100#^^^#100#^^^#100#^^^#100
* Pentacthulhupent, E100#^^^#*#5
* Pentacthulhuhex, E100#^^^#*#6
* Pentacthulhuhept, E100#^^^#*#7
* Gammabixul, <math>200![200,200(1)2]</math>
* Deutero-pentacthulhum, E100#^^^#*#^^^#100
* Trito-pentacthulhum, E100#^^^#*#^^^#*#^^^#100
* Pentacthulhufact, E100(#^^^#)^#100
* Gammatrixul, <math>200![200,200,200(1)2]</math>
* Quarticupentacthulhum, E100(#^^^#)^####100
* Dutetrated-pentacthulhum, E100(#^^^#)^#^^^#100
* Tritetrated-pentacthulhum, E100(#^^^#)^(#^^^#)^(#^^^#)100
* Quadratetrated-pentacthulhum, E100(#^^^#)^^#4
* Quinquatetrated-pentacthulhum, E100(#^^^#)^^#5
* Sexatetrated-pentacthulhum, E100(#^^^#)^^#6
* Septatetrated-pentacthulhum, E100(#^^^#)^^#7
* Octatetrated-pentacthulhum, E100(#^^^#)^^#8
* Terrible pentacthulhum, E100(#^^^#)^^#100
* Dustaculated-terripentacthulhum, E100(#^^^#)^^#>#(#^^^#)^^#100
* Terrisquared pentacthulhum, E100(#^^^#)^^##100
* Terricubed pentacthulhum, E100(#^^^#)^^###100
* Territesserated pentacthulhum, E100(#^^^#)^^####100
* Terripenterated pentacthulhum, E100(#^^^#)^^#####100
* Territoped-pentacthuloogol, {100,100[1[2¬2]2[1\2¬2]2]2}
* Territoped pentacthulhum, E100(#^^^#)^^#^#100
* Dupentated-pentacthuloogol, {100,100[1[1[1[1[2¬2]2]2¬2]2]2¬2]2[1\2¬2]2]2}
* Dupentated-pentacthulhum / pentacthulhutetripso-pentacthulhum, E100(#^^^#)^^(#^^^#)100
* Terrible dupentated-pentacthulhum, E100((#^^^#)^^(#^^^#))^^#100
* Terrisquared dupentated-pentacthulhum, E100((#^^^#)^^(#^^^#))^^##100
* Tripentacthulated-pentacthulhum, E100(((#^^^#)^^(#^^^#))^^(#^^^#))^^(#^^^#)100
* Dustaculated-dupentated-pentacthulhum, E100(#^^^#)^^(#^^^#)>(#^^^#)^^(#^^^#)100
* Pentacthulhu-by-hyperia-tetrated-pentacthulhum, E100(#^^^#)^^(#^^^#*#)100
* Pentacthulhu-by-deutero-hyperia-tetrated-pentacthulhum, E100(#^^^#)^^(#^^^#*##)100
* Pentacthulhu-deutero-pentacthulhutetrate, E100(#^^^#)^^(#^^^#*#^^^#)100
* Pentacthulhu-trito-pentacthulhutetrate, E100(#^^^#)^^(#^^^#*#^^^#*#^^^#)100
* Pentacthulhu-terripentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^#100
* Pentacthulhu-terrisquared-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^##100
* Pentacthulhu-terricubed-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^###100
* Pentacthulhu-territoped-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^#^#100
* Tripentated-pentacthulhum, E100(#^^^#)^^(#^^^#)^^(#^^^#)100
* Quadrapentated-pentacthulhum, E100(#^^^#)^^^#4
* Quinquapentated-pentacthulhum, E100(#^^^#)^^^#5
* Sexapentated-pentacthulhum, E100(#^^^#)^^^#6
* Septapentated-pentacthulhum, E100(#^^^#)^^^#7
* Octapentated-pentacthulhum, E100(#^^^#)^^^#8
* Nonapentated-pentacthulhum, E100(#^^^#)^^^#9
* Decapentated-pentacthulhum, E100(#^^^#)^^^#10
* Pentacthuloodugon, {100,100[1[1\2¬2]3]2}
* Pentacthuldugon / horrible pentacthulhum, E100(#^^^#)^^^#100

=== Part 6.14: <math>f_{\Gamma_1}^2(10)</math> ~ <math>f_{\varphi(2,0,0)}^2(10)</math> ===

* Grand pentacthuldugon, E100(#^^^#)^^^#100#2
* Gamthraxul, <math>200![200(1)3]</math>
* Dutetrated-pentacthuldugon, E100((#^^^#)^^^#)^((#^^^#)^^^#)100
* Terrible pentacthuldugon, E100((#^^^#)^^^#)^^#100
* Terrisquared pentacthuldugon, E100((#^^^#)^^^#)^^##100
* Terrixitried pentacthuldugon / pentacthuldugon-tethrathothitetrate, E100((#^^^#)^^^#)^^#^^#100
* Pentacthuldugon-pentacthulhutetrate, E100((#^^^#)^^^#)^^(#^^^#)100
* Pentacthuldugon-dupentated-pentacthulhutetrate, E100((#^^^#)^^^#)^^(#^^^#)^^(#^^^#)100
* Dupentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Pentacthuldugon-by-hyperia-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#*#)100
* Deutero-pentacthuldugon-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#*(#^^^#)^^^#)100
* Terripentacthuldugon-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^#100
* Tripentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Quadrapentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Pentacthultrigon, E100((#^^^#)^^^#)^^^#100
* Dupentated-pentacthultrigon, E100(((#^^^#)^^^#)^^^#)^^(((#^^^#)^^^#)^^^#)100
* Gappingly / Griddigol, E100((#^^^#)#^^^#)#^^^#)^^((#^^^#^^^#)^^^(#^^^#)100
* Pentacthulootetragon, {100,100[1[1\2¬2]5]2}
* Pentacthultetragon, E100(((#^^^#)^^^#)^^^#)^^^#100
* Pentacthulpentagon, E100((((#^^^#)^^^#)^^^#)^^^#)^^^#100
* Pentacthulhexagon, E100#^^^#>#6
* Pentacthulheptagon, E100#^^^#>#7
* Pentacthuloctagon, E100#^^^#>#8
* Pentacthulennagon, E100#^^^#>#9
* Pentacthuldekagon, E100#^^^#>#10
* Pentacthulooterator, {100,100[1[1\2¬2]1,2]2}
* Pentacthuliterator / pentacthulhum ba'al, E100#^^^#>#100
* Hugexul, 200![200(1)200]
* Kilohugexul, (200![200(1)200])![200(1)200]
* Megahugexul, ((200![200(1)200])![200(1)200])![200(1)200]
* Gigahugexul, (((200![200(1)200])![200(1)200])![200(1)200])![200(1)200]
* Terahugexul, 200(![200(1)200])5
* Petahugexul, 200(![200(1)200])6
* Exahugexul, 200(![200(1)200])7
* Grand Hugexul, 200(![200(1)200])200![200(1)200]+1
* Grand Kilohugexul, 200(![200(1)200])(200![200(1)200])![200(1)200]+1
* Grand Megahugexul, 200(![200(1)200])((200![200(1)200])![200(1)200])![200(1)200]+1
* Grand Gigahugexul, 200(![200(1)200])200(![200(1)200])4+1
* Grand Terahugexul, 200(![200(1)200])200(![200(1)200])5+1
* Grand Petahugexul, 200(![200(1)200])200(![200(1)200])6+1
* Grand Exahugexul, 200(![200(1)200])200(![200(1)200])7+1
* Bigrand Hugexul, 200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1
* Trigrand Hugexul, 200(![200(1)200])200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1+1
* Quadgrand Hugexul, 200(![200(1)200])200(![200(1)200])200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1+1+1
* Quintgrand Hugexul
* Grand pentacthuliterator / great and horrible pentacthulhum, E100#^^^#>#100#2
* Pentacthuliterfact, E100(#^^^#>#)^#100
* Terrible pentacthuliterator, E100(#^^^#>#)^^#100
* Pentacthuliterator-pentacthulhutetrate / pentacthulhum-tetrated-pentacthuliterator, E100(#^^^#>#)^^(#^^^#)100
* Pentacthuldugon-tetrated-pentacthuliterator, E100(#^^^#>#)^^((#^^^#)^^^#)100
* Dupentated-pentacthuliterator, E100(#^^^#>#)^^(#^^^#>#)100
* Horrible pentacthuliterator, E100(#^^^#>#)^^^#100
* Double-horrible pentacthuliterator, E100((#^^^#>#)^^^#)^^^#100
* Pentacthulditerator, E100#^^^#>(#+#)100
* Pentacthultriterator, E100#^^^#>(#+#+#)100
* Pentacthulooquadiator, {100,100[1[1\2¬2]1,5]2}
* Pentacthulquaditerator, E100#^^^#>(#+#+#+#)100
* Pentacthuloogridiator, {100,100[1[1\2¬2]1,1,2]2}
* Pentacthulgriditerator, E100#^^^#>##100
* Superior Hugexul, 200![200(1)200,200]
* Superior Kilohugexul, (200![200(1)200,200])![200(1)200,200]
* Superior Grand Hugexul, 200(![200(1)200,200])200![200(1)200,200]+1
* Superior Bigrand Hugexul, 200(![200(1)200,200])200(![200(1)200,200])200![200(1)200,200]+1+1
* Horrible pentacthulgriditerator, E100(#^^^#>##)^^^#100
* Pentacthuloocubiator, {100,100[1[1\2¬2]1,1,1,2]2}
* Pentacthulcubiculator, E100#^^^#>###100
* Pentacthulquarticulator, E100#^^^#>####100
* Pentacthulquinticulator, E100#^^^#>#####100
* Pentacthulsexticulator, E100#^^^#>#^#6
* Pentacthulsepticulator, E100#^^^#>#^#7
* Godgahlah-turreted-pentacthulhum / pentacthulspatialator, E100#^^^#>#^#100
* Tethrathoth-turreted-pentacthulhum, E100#^^^#>#^^#100
* Tethriterator-turreted-pentacthulhum, E100#^^^#>#^^#>#100
* Tethrigriditer-turreted-tethrathoth, E100#^^^#>#^^#>##100
* Tethrispatialaturreted-pentacthulhum, E100#^^^#>#^^#>#^#100
* Dustaculated-tethrathothiturreted-pentacthulhum, E100#^^^#>#^^#>#^^#100
* Tethracross-turreted-pentacthulhum, E100#^^^#>#^^##100
* Tethracubor-turreted-pentacthulhum, E100#^^^#>#^^###100
* Tethrateron-turreted-pentacthulhum, E100#^^^#>#^^####100
* Tethrapeton-turreted-pentacthulhum, E100#^^^#>#^^#####100
* Tethratope-turreted-pentacthulhum, E100#^^^#>#^^#^#100
* Tethrarxitri-turreted-pentacthulhum, E100#^^^#>#^^#^^#100
* Tethrarxitet-turreted-pentacthulhum, E100#^^^#>#^^#^^#^^#100
* Uningam, <math>f_{\Gamma_{\Gamma_0}}(10)</math>
* Dustaculated-pentacthulhum, E100#^^^#>#^^^#100
* Horrible dustaculated-pentacthulhum, E100(#^^^#>#^^^#)^^^#100
* Horriterated-dustaculated-pentacthulhum, E100#^^^#>(#^^^#+#)100
* Deuterpentacthulhum-turreted-pentacthulhum, E100#^^^#>(#^^^#*#^^^#)100
* Pentacthulhufact-turreted-pentacthulhum, E100#^^^#>(#^^^#)^#100
* Terripentacthulhuturreted-pentacthulhum, E100#^^^#>(#^^^#)^^#100
* Dupentated-pentacthulhuturreted-pentacthulhum, E100#^^^#>(#^^^#)^^(#^^^#)100
* Pentacthuldugon-turreted-pentacthulhum, E100#^^^#>(#^^^#)^^^#100
* Pentacthuliterator-turreted-pentacthulhum, E100#^^^#>#^^^#>#100
* Pentacthulgriditerator-turreted-pentacthulhum, E100#^^^#>#^^^#>##100
* Pentacthulspatialator-turreted-pentacthulhum, E100#^^^#>#^^^#>#^#100
* Bingam, <math>f_{\Gamma_{\Gamma_{\Gamma_0}}}(10)</math>
* Tristaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#100
* Tringam, <math>f_{\Gamma_{\Gamma_{\Gamma_{\Gamma_0}}}}(10)</math>
* Tetrastaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#>#^^^#100
* Quadringam, <math>f_{\varphi(1,1,0)[5]}(10)</math>
* Pentastaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#>#^^^#>#^^^#100
* Quintingam, <math>f_{\varphi(1,1,0)[6]}(10)</math>
* Sextingam, <math>f_{\varphi(1,1,0)[7]}(10)</math>
* Septingam, <math>f_{\varphi(1,1,0)[8]}(10)</math>
* Octingam, <math>f_{\varphi(1,1,0)[9]}(10)</math>
* Noningam / unaddommthet, <math>f_{\varphi(1,1,0)}(10)</math>
* Dekingam, <math>f_{\varphi(1,1,0)[11]}(10)</math>
* Pentacthuloocross, {100,100[1[1\2¬2]1\2]2}
* Pentacthulcross, E100#^^^##100
* ''Bungulus (RedBandServerYT)'' / bikungulus, {100,1002,3} & 10
* Hektingam, <math>f_{\varphi(1,1,0)[101]}(10)</math>
* Bisuperior Hugexul, 200![200(1)200,200,200]
* Bisuperior Kilohugexul, (200![200(1)200,200,200])![200(1)200,200,200
* Bisuperior Grand Hugexul, 200(![200(1)200,200,200])200![200(1)200,200,200]+1
* Bisuperior Bigrand Hugexul, 200(![200(1)200,200,200])200(![200(1)200,200,200])200![200(1)200,200,200]+1+1
* Kilingam, <math>f_{\varphi(1,1,0)[1001]}(10)</math>
* Megingam, <math>f_{\varphi(1,1,0)[10^6+1]}(10)</math>
* Gigingam, <math>f_{\varphi(1,1,0)[10^9+1]}(10)</math>
* Teringam, <math>f_{\varphi(1,1,0)[10^{12}+1]}(10)</math>
* Petingam, <math>f_{\varphi(1,1,0)[10^{15}+1]}(10)</math>
* Exingam, <math>f_{\varphi(1,1,0)[10^{18}+1]}(10)</math>
* Zettingam, <math>f_{\varphi(1,1,0)[10^{21}+1]}(10)</math>
* Yottingam, <math>f_{\varphi(1,1,0)[10^{24}+1]}(10)</math>
* Grand pentacthulcross, E100#^^^##100#2
* Deutero-pentacthulcross, E100#^^^##*#^^^##100
* Dutetrated-pentacthulcross, E100(#^^^##)^(#^^^##)100
* Terrible pentacthulcross, E100(#^^^##)^^#100
* Dupentated-pentacthulcross, E100(#^^^##)^^(#^^^##)100
* Horrible pentacthulcross, E100(#^^^##)^^^#100
* Horriterated pentacthulcross, E100(#^^^##)^^^#>#100
* Dustaculated-horripentacthulcross, E100(#^^^##)^^^#>(#^^^##)^^^#100
* Pentacthulooducross, {100,100[1[1\2¬2]1\3]2}
* Pentacthulducross, E100(#^^^##)^^^##100
* Pentacthultricross, E100((#^^^##)^^^##)^^^##100
* Pentacthulootetracross, {100,100[1[1\2¬2]1\5]2}
* Pentacthultetracross, E100#^^^##>#4
* Pentacthulpentacross, E100#^^^##>#5
* Pentacthulootercross, {100,100[1[1\2¬2]1\1,2]2}
* Pentacthulitercross, E100#^^^##>#100
* Dustaculated-pentacthulcross, E100#^^^##>#^^^##100
* Menger sponge, E[20]3###^^^###3
* Tristaculated-pentacthulcross, E100#^^^##>#^^^##>#^^^##100
* Baddommthet, <math>f_{\varphi(1,2,0)}(10)</math>
* Pentacthuloocubor, {100,100[1[1\2¬2]1\1\2]2}
* Pentacthulcubor, E100#^^^###100
* Pentacthulitercubor, E100#^^^###>#100
* Dustaculated-pentacthulcubor, E100#^^^###>#^^^###100
* Traddommthet, <math>f_{\varphi(1,3,0)}(10)</math>
* Pentacthulteron, E100#^^^####100
* Quadraddommthet, <math>f_{\varphi(1,4,0)}(10)</math>
* Pentacthulpeton, E100#^^^#^#5
* Quintaddommthet, <math>f_{\varphi(1,5,0)}(10)</math>
* Pentacthulhexon, E100#^^^#^#6
* Sextaddommthet, <math>f_{\varphi(1,6,0)}(10)</math>
* Pentacthulhepton, E100#^^^#^#7
* Septaddommthet, <math>f_{\varphi(1,7,0)}(10)</math>
* Pentacthul-ogdon, E100#^^^#^#8
* Octaddommthet, <math>f_{\varphi(1,8,0)}(10)</math>
* Pentacthulennon, E100#^^^#^#9
* Nonaddommthet, <math>f_{\varphi(1,9,0)}(10)</math>
* Pentacthuloodekon, {100,100[1[1\2¬2]1\1\1\1\1\1\1\1\1\2]2}
* Pentacthuldekon, E100#^^^#^#10
* Dekaddommthet, <math>f_{\varphi(1,\omega,0)}(10)</math>
* Pentacthulootope, {100,100[1[1\2¬2]1[2¬2]2]2}
* Pentacthultope / pentacthulhecton, E100#^^^#^#100
* Hektaddommthet, <math>f_{\varphi(1,100,0)}(10)</math>
* Kiladdommthet, <math>f_{\varphi(1,1000,0)}(10)</math>
* Megaddommthet, <math>f_{\varphi(1,10^6,0)}(10)</math>
* Gigaddommthet, <math>f_{\varphi(1,10^9,0)}(10)</math>
* Teraddommthet, <math>f_{\varphi(1,10^{12},0)}(10)</math>
* Petaddommthet, <math>f_{\varphi(1,10^{15},0)}(10)</math>
* Exaddommthet, <math>f_{\varphi(1,10^{18},0)}(10)</math>
* Zettaddommthet, <math>f_{\varphi(1,10^{21},0)}(10)</math>
* Yottaddommthet, <math>f_{\varphi(1,10^{24},0)}(10)</math>
* Pentacthultopothoth, E100#^^^(#^#*#)100
* Pentacthultopocross, E100#^^^(#^#*##)100
* Pentacthultopodeus, E100#^^^(#^#*#^#)100
* Pentacthultopotruce, E100#^^^(#^#*#^#*#^#)100
* Pentacthuloolattitope, {100,100[1[1\2¬2]1[3¬2]2]2}
* Pentacthulattitope, E100#^^^#^##100
* Pentacthuloocubitope, {100,100[1[1\2¬2]1[4¬2]2]2}
* Pentacthulcubitope, E100#^^^#^###100
* Pentacthuloogodgathor, {100,100[1[1\2¬2]1[1,2¬2]2]2}
* Pentacthulto-godgathor, E100#^^^#^#^#100
* Pentacthulto-tethrathoth, E100#^^^#^^#100
* Pentacthulootethrinoogol, {100,100[1[1\2¬2]1[1[1\2]2¬2]2]2}
* Pentacthularxitri / pentacthulto-pentacthulhum, E100#^^^#^^^#100
* Pentacthuloogarxitri, {100,100[1[1\2¬2]1[1[1[1\2¬2]2]2¬2]2]2}
* Pentacthularxitet, E100#^^^#^^^#^^^#100
* Pentacthuloogarxipent, {100,5[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxideck, {100,10[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxicose, {100,20[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxipenine, {100,50[1[1\2¬2]1[1\2¬2]2]2}
* Hexacthulhum / pentacthularxihect, E100#^^^^#100
* ''Quadrunculus'', <math>X \uparrow \uparrow \uparrow \uparrow 100 \& 10 </math>

=== Part 6.15: <math>f_{\varphi(2,0,0)}^2(10)</math> ~ <math>f_{\varphi(\omega,0,0)}^2(10)</math> ===

* Grand hexacthulhum, E100#^^^^#100#2
* Grangol-carta-hexacthulhum, E100#^^^^#100#100
* Hexacthulhum-by-deuteron, E100#^^^^#100#^^^^#100
* Hexacthulhufact, E100(#^^^^#)^#100
* Terrible hexacthulhum, E100(#^^^^#)^^#100
* Horrible hexacthulhum, E100(#^^^^#)^^^#100
* Duhexated-hexacthulhum, E100(#^^^^#)^^^(#^^^^#)100
* Hexadeucthulhum / horrendous hexacthulhum, E100(#^^^^#)^^^^#100
* Hexacthuliterator, E100#^^^^#>#100
* Hugebixul, 200![200(1)200(1)200]
* Kilohugebixul, (200![200(1)200(1)200])![200(1)200(1)200]
* Megahugebixul, ((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]
* Gigahugebixul, (((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]
* Grand Hugebixul, 200(![200(1)200(1)200])200![200(1)200(1)200]+1
* Grand Kilohugebixul, 200(![200(1)200(1)200])(200![200(1)200(1)200])![200(1)200(1)200]+1
* Grand Megahugebixul, 200(![200(1)200(1)200])((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]+1
* Grand Gigahugebixul, 200(![200(1)200(1)200])200(![200(1)200(1)200])4+1
* Bigrand Hugebixul, 200(![200(1)200(1)200])200(![200(1)200(1)200])200![200(1)200(1)200]+1+1
* Trigrand Hugebixul
* Superior Hugebixul, 200![200(1)200(1)200,200]
* Superior Kilohugebixul, (200![200(1)200(1)200,200])![200(1)200(1)200,200]
* Superior Megahugebixul, ((200![200(1)200(1)200,200])![200(1)200(1)200,200])![200(1)200(1)200,200]
* Superior Grand Hugebixul, 200(![200(1)200(1)200,200])200![200(1)200(1)200,200]+1
* Superior Grand Kilohugebixul, 200(![200(1)200(1)200,200])(200![200(1)200(1)200,200])![200(1)200(1)200,200]+1
* Superior Grand Megahugebixul, 200(![200(1)200(1)200,200])200(![200(1)200(1)200,200])3+1
* Superior Bigrand Hugebixul, 200(![200(1)200(1)200,200])200(![200(1)200(1)200,200])200![200(1)200(1)200,200]+1+1
* Dustaculated hexacthulhum, E100#^^^^#>#^^^^#100
* Hexacthulcross, E100#^^^^##100
* Bisuperior Hugebixul, 200![200(1)200(1)200,200,200]
* Bisuperior Kilohugebixul, (200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]
* Bisuperior Megahugebixul, ((200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]
* Bisuperior Grand Hugebixul, 200(![200(1)200(1)200,200,200])200![200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugebixul, 200(![200(1)200(1)200,200,200])(200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]+1
* Bisuperior Grand Megahugebixul, 200(![200(1)200(1)200,200,200])200(![200(1)200(1)200,200,200])3+1
* Bisuperior Bigrand Hugebixul
* Hexacthulcubor, E100#^^^^###100
* Hexacthulhexon, E100(#^^^^#^6)100
* Hexacthuliterhexon, E100#^^^^(#^6)>#100
* Hexacthultope / hexacthulhecton, E100#^^^^#^#100
* Hexacthularxitri, E100#^^^^#^^^^#100
* Joe pellinger, 203^431,112,937#^^^^########^^^^######>#^#203,431,112,937
* Grand joe pellinger, 203^431,112,937#^^^^########^^^^######>#^#203,431,112,937#2
* Heptacthulhum / hexacthularxihect, E100#{5}#100
* Hepacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* ''Quintunculus'', <math>\{X,100,5\}\ \&\ 10</math>
* Heptacthuliterator / heptacthulhum ba'al, E100#{5}#>#100
* Hugetrixul, 200![200(1)200(1)200(1)200]
* Kilohugetrixul, (200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]
* Megahugetrixul, ((200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]
* Gigahugetrixul, 200(![200(1)200(1)200(1)200])4
* Grand Hugetrixul, 200(![200(1)200(1)200(1)200])200![200(1)200(1)200(1)200]+1
* Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200])(200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]+1
* Grand Megahugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])3+1
* Grand Gigahugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])4+1
* Bigrand Hugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])200![200(1)200(1)200(1)200]+1+1
* Trigrand Hugetrixul
* Superior Hugetrixul, 200![200(1)200(1)200(1)200,200]
* Superior Kilohugetrixul, (200![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200]
* Superior Megahugetrixul, ((200![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200]
* Superior Grand Hugetrixul, 200(![200(1)200(1)200(1)200,200])200![200(1)200(1)200(1)200,200]+1
* Superior Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200,200])2+1
* Superior Grand Megahugetrixul, 200(![200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200,200])3+1
* Superior Bigrand Hugetrixul
* Bisuperior Hugetrixul, 200![200(1)200(1)200(1)200,200,200]
* Bisuperior Kilohugetrixul, (200![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200]
* Bisuperior Megahugetrixul, ((200![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200]
* Bisuperior Grand Hugetrixul, 200(![200(1)200(1)200(1)200,200,200])200![200(1)200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200,200,200])200(![200(1)200(1)200(1)200,200,200])2+1
* Bisuperior Grand Megahugetrixul, 200(![200(1)200(1)200(1)200,200,200])200(![200(1)200(1)200(1)200,200,200])3+1
* Bisuperior Bigrand Hugetrixul
* Honiara, E[13]Mentalize#{5}###^^#>#^#^^#>(#^^^^#)^^^(#^^^^#)>(#^#*#+#) (Hyper pectrol number)
* Ogdacthulhum / heptacthularxihect, E100#{6}#100
* Ogdacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Ogdacthulhufact, E100(#{6}#)^#100
* Ogdacthulhum-ipso-godgahlah, E100(#{6}#)^#^#100
* Dutetrated ogdacthulhum, E100(#{6}#)^(#{6}#)100
* Ogdacthuliterator, E100#{6}#>#100
* Hugequaxul, 200![200(1)200(1)200(1)200(1)200]
* Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]
* Megahugequaxul, ((200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]
* Gigahugequaxul, 200(![200(1)200(1)200(1)200(1)200])4
* Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200])200![200(1)200(1)200(1)200(1)200]+1
* Grand Kilohugequaxul, 200(![200(1)200(1)200(1)200(1)200])(200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]+1
* Grand Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200(1)200])3+1
* Grand Gigahugequaxul, 200(![200(1)200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200(1)200])4+1
* Bigrand Hugequaxul
* Trigrand Hugequaxul
* Superior Hugequaxul, 200![200(1)200(1)200(1)200(1)200,200]
* Superior Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200(1)200,200]
* Superior Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])3
* Superior Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200![200(1)200(1)200(1)200(1)200,200]+1
* Superior Grand Kilohugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200(1)200,200])2+1
* Superior Grand Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200(1)200,200])3+1
* Superior Bigrand Hugequaxul
* Bisuperior Hugequaxul, 200![200(1)200(1)200(1)200(1)200,200,200]
* Bisuperior Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200(1)200,200,200]
* Bisuperior Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200,200])3
* Bisuperior Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200,200,200])200![200(1)200(1)200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugequaxul
* Bisuperior Grand Megahugequaxul
* Bisuperior Bigrand Hugequaxul
* Ennacthulhum / ogdacthularxihect, E100#{7}#100
* Ennacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Grand ennacthulhum, E100#{7}#100#2
* Grangol-carta-ennacthulhum, E100#{7}#100#100
* Godgahlah-carta-ennacthulhum, E100#{7}#100#^#100
* Tethrathoth-carta-ennactulhum, E100#{7}#100#^^#100
* Pentacthulhum-carta-ennacthulhum, E100#{7}#100#^^^#100
* hexacthulhum-carta-ennacthulhum, E100#{7}#100#^^^^#100
* Heptacthulhum-carta-ennacthulhum, E100#{7}#100#{5}#100
* Ogdacthulhum-carta-ennacthulhum, E100#{7}#100#{6}#100
* Ennacthulhum-carta-ennacthulhum / Ennacthulhum-by-deuteron, E100#{7}#100#{7}#100
* Deutero-ennacthulhum, E100#{7}#*#{7}#100
* Ennacthulhufact, E100(#{7}#)^#100
* Terrible ennacthulhum, E100(#{7}#)^^#100
* Horrible ennacthulhum, E100(#{7}#)^^^#100
* Horrendous ennacthulhum, E100(#{7}#)^^^^#100
* Ennacthuliterator / ennacthulhum ba'al, E100#{7}#>#100
* Grand ennacthuliterator / great and ennorredous ennacthulhum, E100#{7}#>#100#2
* Dustaculated ennacthulhum, E100#{7}#>#{7}#100
* Ennacthulcross, E100#{7}##100
* Ennacthulcubor, E100#{7}###100
* Ennacthultope, E100#{7}#^#100
* Ennacthularxitri, E100#{7}#{7}#100
* Dekacthulhum / ennacthularxihect, E100#{8}#100
* Dekacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Ennacthularxigigas, E100#{8}#500
* Ennacthularxichill, E100#{8}#1000
* Grand dekacthulhum, E100#{8}#100#2 = E100#{8}#dekacthulhum
* Deutero-dekacthulhum, E100#{8}#*#{8}#100
* Dekacthulcross, E100#{8}##100
* Dekacthularxitri / dekacthulto-dekacthulhum, E100#{8}#{8}#100
* Dekacthularxitet, E100#{8}#{8}#{8}#100 = E100#{9}#4
* Dekacthularxihect, E100#{9}#100
* ''Tridecatrix'', {10,10,10} & 10
* Goliath, E100#{10}#100 = E100#{#}#10
* Backongulus, {10,10[1[2\2¬2]2]2}
* Triadekacthuloogol, {100,10[1[2\2¬2]2]2}
* Icosacthuloogol, {100,17[1[2\2¬2]2]2}
* Golligog, E100#{50}#100 = E100#{#}#50
* Gollinoogol, {100,49[1[2\2¬2]2]2}
* Godsgodgulus, E100#{#}#100 = E100#{100}#100
* Godsgodgoogol, {100,99[1[2\2¬2]2]2}
* Godsgoduloogol, {100,100[1[2\2¬2]2]2}
* Joeligog, E100#{#}#203 = E100#{203}#100
* Gigantorgog, E100#{#}#500 = E100#{500}#100
* Godsgodgoogolchime, {100,999[1[2\2¬2]2]2}
* Godsgodgoogoltoll, {100,9999[1[2\2¬2]2]2}
* Godsgodgulusgong, E100,000#{#}#100,000
* Godsgodgoogolgong, {100,99999[1[2\2¬2]2]2}
* Pseuligog, E100#{#}#44435622 = E100#{44435622}#100
* Popacthulhum, E100#{#}#P = E100#{P}#100 where P is the world population right now (increases throughout time)
* Colossigog, E100#{#}#50,000,000,000,000,000 = E100#{50,000,000,000,000,000}#100
* Colossoogol, {100,5*10^16[1[2\2¬2]2]2}

=== Part 6.16: <math>f_{\varphi(\omega,0,0)}^2(10)</math> ~ <math>f_{\varphi(1,0,0,0)}^2(10)</math> ===

* Grand godsgodgulus, E100#{#}#100#2
* Grand grand godsgodgulus, E100#{#}#100#3
* Triple grand godsgodgulus, E100#{#}#100#4
* Quadruple grand godsgodgulus, E100#{#}#100#5
* Grangol-carta-godsgodgulus, E100#{#}#100#100
* Greagol-carta-godsgodgulus, E100#{#}#100#100#100
* Gigangol-carta-godsgodgulus, E100#{#}#100#100#100#100
* Godsgodgulus-by-deuteron, E100#{#}#100#{#}#100
* Godsgodgulus-by-triton, E100#{#}#100#{#}#100#{#}#100
* Godsgodgulus-by-teterton, E100#{#}#100#{#}#100#{#}#100#{#}#100
* Godsgodgulus-by-hyperion, E100#{#}#*#100
* Godsgodgulus-by-pentacthulhum, E100#{#}#*#^^^#100
* Deutero-godsgodgulus, E100#{#}#*#{#}#100
* Godsgodgulfact, E100(#{#}#)^#100
* Grideutergodsgodgulus / quadrata-godsgodgulus, E100(#{#}#)^##100
* Kubicugodsgodgulus / kubiku-godsgodgulus, E100(#{#}#)^###100
* Quarticugodsgodgulus / quarticu-godsgodgulus, E100(#{#}#)^####100
* Quinticu-godsgodgulus, E100(#{#}#)^#^#5
* Sexticu-godsgodgulus, E100(#{#}#)^#^#6
* Septicu-godsgodgulus, E100(#{#}#)^#^#7
* Octicu-godsgodgulus, E100(#{#}#)^#^#8
* Nonicu-godsgodgulus, E100(#{#}#)^#^#9
* Decicu-godsgodgulus, E100(#{#}#)^#^#10
* Godsgodgulipso-godgahlah, E100(#{#}#)^#^#100
* Godsgodgulipso-tethrathoth, E100(#{#}#)^#^^#100
* Godsgodgulipso-pentacthulhum, E100(#{#}#)^#^^^#100
* Godsgodgulipso-hexacthulhum, E100(#{#}#)^#^^^^#100
* Godsgodgulipso-heptacthulhum, E100(#{#}#)^#{5}#100
* Godsgodgulipso-odgacthulhum, E100(#{#}#)^#{6}#100
* Godsgodgulipso-ennacthulhum, E100(#{#}#)^#{7}#100
* Godsgodgulipso-deckacthulhum, E100(#{#}#)^#{8}#100
* Dutetrated-godsgodgulus, E100(#{#}#)^(#{#}#)100
* Tritetrated-godsgodgulus, E100(#{#}#)^(#{#}#)^(#{#}#)100
* Quadratetrated-godsgodgulus, E100(#{#}#)^(#{#}#)^(#{#}#)^(#{#}#)100
* Quinquatetrated-godsgodgulus, E100(#{#}#)^^#5
* Sexatetrated-godsgodgulus, E100(#{#}#)^^#6
* Septaquatetrated-godsgodgulus, E100(#{#}#)^^#7
* Octatetrated-godsgodgulus, E100(#{#}#)^^#8
* Nonatetrated-godsgodgulus, E100(#{#}#)^^#9
* Decatetrated-godsgodgulus, E100(#{#}#)^^#10
* Terrible godsgodgulus, E100(#{#}#)^^#100
* Terrisquared godsgodgulus, E100(#{#}#)^^##100
* Terricubed godsgodgulus, E100(#{#}#)^^###100
* Territesserated godsgodgulus, E100(#{#}#)^^####100
* Territoped godsgodgulus, E100(#{#}#)^^#^#100
* Tethrathoth-tetrated godsgodgulus, E100(#{#}#)^^#^^#100
* Pentacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#^^^#100
* Hexacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#^^^^#100
* Heptacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#{5}#100
* Dupentated godsgodgulus, E100(#{#}#)^^(#{#}#)100
* Tripentated godsgodgulus, E100(#{#}#)^^(#{#}#)^^(#{#}#)100
* Quadrapentated godsgodgulus, E100(#{#}#)^^^#4
* Horrible godsgodgulus, E100(#{#}#)^^^#100
* Horrendous godsgodgulus, E100(#{#}#)^^^^#100
* Heptorrendous godsgodgulus, E100(#{#}#){5}#100
* Ogdorrendous godsgodgulus, E100(#{#}#){6}#100
* Ennorrendous godsgodgulus, E100(#{#}#){7}#100
* Dekorrendous godsgodgulus, E100(#{#}#){8}#100
* Godsgodeugulus, E100(#{#}#){#}#100
* Godsgodeugulusfact, E100((#{#}#){#}#)^#100
* Terrible godsgodeugulus, E100((#{#}#){#}#)^^#100
* Horrible godsgodeugulus, E100((#{#}#){#}#)^^^#100
* Horrendous godsgodeugulus, E100((#{#}#){#}#)^^^^#100
* Godsgotrigulus, E100((#{#}#){#}#){#}#100
* Godsgodguliterator / godsgodgulus ba'al, E100#{#}#>#100
* Grand godsgodguliterator / great and blasphemous godsgodgulus, E100#{#}#>#100#2
* Godsgodgulitertri, E100#{#}#>#100#{#}#>#100
* Godsgodgulitera-by-hyperion, E100#{#}#>#*#100
* Deutero-godsgodguliterator, E100#{#}#>#*#{#}#>#100
* Godsgodguliterfact, E100(#{#}#>#)^#100
* Terrible godsgodguliterator, E100(#{#}#>#)^^#100
* Horrible godsgodguliterator, E100(#{#}#>#)^^^#100
* Horrendous godsgodguliterator, E100(#{#}#>#)^^^^#100
* Godsgodgudous godsgodguliterator, E100(#{#}#>#){#}#100
* Godsgodgucubiterator, E100#{#}#>###100
* Tethrathoth-tetrated godsgodgulus, E100#{#}#>#^^#100
* Pentacthulhum-tetrated godsgodgulus, E100#{#}#>#^^^#100
* Hexacthulhum-tetrated godsgodgulus, E100#{#}#>#^^^^#100
* Dustaculated godsgodgulus, E100#{#}#>#{#}#100
* Tristaculated godsgodgulus, E100#{#}#>#{#}#>#{#}#100
* Tetrastaculated godsgodgulus, E100#{#}#>#{#}#>#{#}#>#{#}#100
* Pentastaculated godsgodgulus, E100#{#}##5
* Hexastaculated godsgodgulus, E100#{#}##6
* Heptastaculated godsgodgulus, E100#{#}##7
* Ogdastaculated godsgodgulus, E100#{#}##8
* Ennastaculated godsgodgulus, E100#{#}##9
* Dekastaculated godsgodgulus, E100#{#}##10
* Godsgodgulcross, E100#{#}##100
* Grand godsgodgulcross, E100#{#}##100#2
* Godsgodgulcross-by-deuteron, E100#{#}##100#{#}##100
* Godsgodgulcross-by-hyperion, E100#{#}##*#100
* Godsgodgulcrossafact, E100(#{#}##)^#100
* Terrible godsgodgulcross, E100(#{#}##)^^#100
* Horrible godsgodgulcross, E100(#{#}##)^^^#100
* Horrendous godsgodgulcross, E100(#{#}##)^^^^#100
* Godsgodgulcro-godsgodgulus, E100(#{#}##){#}#100
* Godsgodguldeucross, E100(#{#}##){#}##100
* Godsgodgultricross, E100#{#}##>#3
* Godsgodgultercross, E100#{#}##>#100
* Godsgodgugridtercross, E100#{#}##>##100
* Dustaculated godsgodgulcross, E100#{#}##>#{#}##100
* Tristaculated godsgodgulcross, E100#{#}###3
* Tetrastaculated godsgodgulcross, E100#{#}###4
* Godsgodgulcubor, E100#{#}###100
* Godsgodgulteron, E100#{#}####100
* Godsgodgultope, E100#{#}#^#100
* Godsgodarxitri, E100#{#}#{#}#100
* Godsgodarxitet, E100#{#}#{#}#{#}#100
* Godsgodgulhenus, E100#{#+1}#100
* Godsgodguliterhenus, E100#{#+1}#>#100
* Godsgodgulhencross, E100#{#+1}##100
* Godsgodgulhencubor, E100#{#+1}###100
* Godsgodgulhentope, E100#{#+1}#^#100
* Godsgodeus, E100#{#+#}#100
* Godsgotreus, E100#{#+#+#}#100
* Godsgoquadeus, E100#{#+#+#+#}#100
* Godsgridoogol, {100,100[1[3\2¬2]2]2}
* Godskubioogol, {100,100[1[4\2¬2]2]2}
* Godsquartioogol, {100,100[1[5\2¬2]2]2}
* Centuroogol, {100,100[1[1,2\2¬2]2]2}
* The centurion, E100#{#^#}#100
* Super centurion, E100#{#^^#}#100
* Pentacthulhu-centurion, E100#{#^^^#}#100
* Hexacthulhu-centurion, E100#{#^^^^#}#100
* Ohmygosh-ohmygosh-ohmygooosh / godsgodgul-centurion, E100#{#{#}#}#100
* Bexommthet, <math>f_{\theta(\Omega^2,0)}(10)</math>
* Blasphemorbackulus, {10,10[1[1\3¬2]2]2}
* Blasphemorgulus, E100{#,#,1,2}100
* ''Gonguldeus'', {10,100,1,2} & 10
* Blasphemorgoogol, {100,100[1[1\3¬2]2]2}

=== Part 6.17: <math>f_{\varphi(1,0,0,0)}^2(10)</math> ~ <math>f_{\varphi(1,0,0,0,0)}^2(10)</math> ===

* Grand blasphemorgulus, E100{#,#,1,2}100#2
* Grand grand blasphemorgulus, E100{#,#,1,2}100#3
* Grangol-carta-blasphemorgulus, E100{#,#,1,2}100#100
* Greagol-carta-blasphemorgulus, E100{#,#,1,2}100#100#100
* Blasphemorgulus-by-deuteron, E100{#,#,1,2}100{#,#,1,2}100
* Blasphemorgulus-by-hyperion, E100{#,#,1,2}*#100
* Deutero-blasphemorgulus, E100{#,#,1,2}*{#,#,1,2}100
* Blasphemorgulfact, E100({#,#,1,2})^#100
* Terrible blasphemorgulus, E100({#,#,1,2})^^#100
* Horrible blasphemorgulus, E100({#,#,1,2})^^^#100
* Horrendous blasphemorgulus, E100({#,#,1,2})^^^^#100
* Blasphemormygosh-blasphemormygosh, E100({#,#,1,2}){{#,#,1,2}}({#,#,1,2})100
* <nowiki>Tweilasphemorgue, E100{{#,#,1,2},100,1,2}100</nowiki>
* Frielasphemorgue, E100{#,#+1,1,2}3
* Fiorilasphemorgue, E100{#,#+1,1,2}4
* Finnasphemorgue, E100{#,#+1,1,2}5
* Sexasphemorgue, E100{#,#+1,1,2}6
* Sjournalasphemorgue, E100{#,#+1,1,2}7
* Attalasphemorgue, E100{#,#+1,1,2}8
* Neiulasphemorgue, E100{#,#+1,1,2}9
* Tenasphemorgue, E100{#,#+1,1,2}10
* <nowiki>Blasphemorguliterator, E100#{{1}}#>#100</nowiki>
* Hundrelasphemorgue, E100{#,#+1,1,2}100
* Enormaxul, 200![200(2)200]
* Thouselasphemorgue, E100{#,#+1,1,2}1,000
* Milliasphemorgue, E100{#,#+1,1,2}1,000,000
* Kiloenormaxul, (200![200(2)200])![200(2)200]
* Megaenormaxul, ((200![200(2)200])![200(2)200])![200(2)200]
* Gigaenormaxul, (((200![200(2)200])![200(2)200])![200(2)200])![200(2)200]
* Teraenormaxul, 200(![200(2)200])5
* Petaenormaxul, 200(![200(2)200])6
* Exaenormaxul, 200(![200(2)200])7
* Grand Enormaxul, 200(![200(2)200])200![200(2)200]+1
* Grand Kiloenormaxul, 200(![200(2)200])(200![200(2)200])![200(2)200]+1
* Grand Megaenormaxul, 200(![200(2)200])((200![200(2)200])![200(2)200])![200(2)200]+1
* Grand Gigaenormaxul, 200(![200(2)200])200(![200(2)200])4+1
* Grand Teraenormaxul, 200(![200(2)200])200(![200(2)200])5+1
* Grand Petaenormaxul, 200(![200(2)200])200(![200(2)200])6+1
* Grand Exaenormaxul, 200(![200(2)200])200(![200(2)200])7+1
* Bigrand Enormaxul, 200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1
* Bigrand Kiloenormaxul, 200(![200(2)200])200(![200(2)200])(200![200(2)200])![200(2)200]+1+1
* Bigrand Megaenormaxul, 200(![200(2)200])200(![200(2)200])((200![200(2)200])![200(2)200])![200(2)200]+1+1
* Trigrand Enormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1+1
* Trigrand Kiloenormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])2+1+1+1
* Trigrand Megaenormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])3+1+1+1
* Quadgrand Enormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1+1+1
* Quintgrand Enormaxul
* Superior Enormaxul, 200![200(2)200,200]
* Superior Kiloenormaxul, (200![200(2)200,200])![200(2)200,200]
* Superior Megaenormaxul, ((200![200(2)200,200])![200(2)200,200])![200(2)200,200]
* Superior Gigaenormaxul, (((200![200(2)200,200])![200(2)200,200])![200(2)200,200])![200(2)200,200]
* Superior Grand Enormaxul, 200(![200(2)200,200])200![200(2)200,200]+1
* Superior Grand Kiloenormaxul, 200(![200(2)200,200])(200![200(2)200,200])![200(2)200,200]+1
* Superior Grand Megaenormaxul, 200(![200(2)200,200])((200![200(2)200,200])![200(2)200,200])![200(2)200,200]+1
* Superior Grand Gigaenormaxul, 200(![200(2)200,200])(((200![200(2)200,200])![200(2)200,200])![200(2)200,200])![200(2)200,200]+1
* Superior Bigrand Enormaxul, 200(![200(2)200,200])200(![200(2)200,200])200![200(2)200,200]+1+1
* Superior Trigrand Enormaxul, 200(![200(2)200,200])200(![200(2)200,200])200(![200(2)200,200])200![200(2)200,200]+1+1+1
* Bisuperior Enormaxul, 200![200(2)200,200,200]
* Bisuperior Kiloenormaxul, (200![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Megaenormaxul, ((200![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Gigaenormaxul, (((200![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Grand Enormaxul, 200(![200(2)200,200,200])200![200(2)200,200,200]+1
* Bisuperior Grand Kiloenormaxul, 200(![200(2)200,200,200])(200![200(2)200,200,200])![200(2)200,200,200]+1
* Bisuperior Grand Megaenormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])3+1
* Bisuperior Grand Gigaenormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])4+1
* Bisuperior Bigrand Enormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])200![200(2)200,200,200]+1+1
* Bisuperior Trigrand Enormaxul
* ''Ludicriss'', E100&(1)100
* ''Grand ludicriss'', E100&(1)100#2
* ''Blasphemorgulcross'', <nowiki>E100#{{1}}##100</nowiki>
* ''Agoraphobia'', E100&(&(&(...(&(&({#,#,1,2})))...))) with 100 &'s ~ E100#*^#100
* ''Gongultreus'', {10,100,1,3} & 10
* ''Grand agoraphobia'', E100&(&(...&({#,#,1,2})... ))100 w/agoraphobia &'s
* ''Blasphemorgulcubor'', <nowiki>E100#{{1}}###100</nowiki>
* ''Astralthrathoth'', E100#*^^#100
* ''Blasphemorgultope'', <nowiki>E100#{{1}}#^#100</nowiki>
* ''Blasphemorgularxitri'', <nowiki>E100#{{1}}#{{1}}#100</nowiki>
* ''Blasphemordeugulus'', <nowiki>E100#{{2}}#100</nowiki>
* ''Mulporatrix'', {10,100,2,2} & 10
* ''Tethrathoth-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^#100</nowiki>''
* ''Pentacthulhum-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^^#100</nowiki>''
* ''Hexacthulhum-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^^^#100</nowiki>''
* ''Godsgodgulus-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#{#}#100</nowiki>''
* ''Blasphemorgulus-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#{{1}}#100</nowiki>''
* ''Blasphemordeugulus-by-deuteron, <nowiki>E100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-triton, <nowiki>E100#{{2}}#100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-teterton, <nowiki>E100#{{2}}#100#{{2}}#100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-hyperion, <nowiki>E100#{{2}}#*#100</nowiki>''
* ''Blasphemortrigulus'', <nowiki>E100#{{3}}#100</nowiki>
* ''Humingulus'', {10,10,100,2} & 10
* ''Deusus-godsgodgogle'', <nowiki>E100#{{#}}#100</nowiki>
* ''Gongultreus'', {10,100,1,3} & 10
* ''Trilasphemorgulus'' / Blasphemorguldeus, <nowiki>E100#{{{1}}}#100</nowiki>
* Enormabixul, 200![200(2)200(2)200]
* Kiloenormabixul, (200![200(2)200(2)200])![200(2)200(2)200]
* Megaenormabixul, ((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]
* Gigaenormabixul, (((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]
* Grand Enormabixul, 200(![200(2)200(2)200])200![200(2)200(2)200]+1
* Grand Kiloenormabixul, 200(![200(2)200(2)200])(200![200(2)200(2)200])![200(2)200(2)200]+1
* Grand Megaenormabixul, 200(![200(2)200(2)200])((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]+1
* Grand Gigaenormabixul, 200(![200(2)200(2)200])200(![200(2)200(2)200])4+1
* Bigrand Enormabixul, 200(![200(2)200(2)200])200(![200(2)200(2)200])200![200(2)200(2)200]+1+1
* Trigrand Enormabixul
* Superior Enormabixul, 200![200(2)200(2)200,200]
* Superior Kiloenormabixul, (200![200(2)200(2)200,200])![200(2)200(2)200,200]
* Superior Megaenormabixul, ((200![200(2)200(2)200,200])![200(2)200(2)200,200])![200(2)200(2)200,200]
* Superior Grand Enormabixul, 200(![200(2)200(2)200,200])200![200(2)200(2)200,200]+1
* Superior Grand Kiloenormabixul, 200(![200(2)200(2)200,200])(200![200(2)200(2)200,200])![200(2)200(2)200,200]+1
* Superior Grand Megaenormabixul, 200(![200(2)200(2)200,200])200(![200(2)200(2)200,200])3+1
* Superior Bigrand Enormabixul, 200(![200(2)200(2)200,200])200(![200(2)200(2)200,200])200![200(2)200(2)200,200]+1+1
* Bisuperior Enormabixul, 200![200(2)200(2)200,200,200]
* Bisuperior Kiloenormabixul, (200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]
* Bisuperior Megaenormabixul, ((200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]
* Bisuperior Grand Enormabixul, 200(![200(2)200(2)200,200,200])200![200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormabixul, 200(![200(2)200(2)200,200,200])(200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]+1
* Bisuperior Grand Megaenormabixul, 200(![200(2)200(2)200,200,200])200(![200(2)200(2)200,200,200])3+1
* Bisuperior Bigrand Enormabixul
* ''Blasphemordeuguldeus'', <nowiki>E100#{{{2}}}#100</nowiki>
* ''Treusus-godsgodgogle'', <nowiki>E100#{{{#}}}#100</nowiki>
* ''Humangulus'', {10,10,100,3} & 10
* ''Blasphemorgultruce'', <nowiki>E100#{{{{1}}}}#100</nowiki>
* ''Gongulquadeus'', {10,100,1,4} & 10
* Enormatrixul, 200![200(2)200(2)200(2)200]
* Kiloenormatrixul, (200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]
* Megaenormatrixul, ((200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]
* Gigaenormatrixul, 200(![200(2)200(2)200(2)200])4
* Grand Enormatrixul, 200(![200(2)200(2)200(2)200])200![200(2)200(2)200(2)200]+1
* Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200])(200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]+1
* Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])3+1
* Grand Gigaenormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])4+1
* Bigrand Enormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])200![200(2)200(2)200(2)200]+1+1
* Trigrand Enormatrixul
* Superior Enormatrixul, 200![200(2)200(2)200(2)200,200]
* Superior Kiloenormatrixul, (200![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200]
* Superior Megaenormatrixul, ((200![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200]
* Superior Grand Enormatrixul, 200(![200(2)200(2)200(2)200,200])200![200(2)200(2)200(2)200,200]+1
* Superior Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200,200])2+1
* Superior Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200,200])3+1
* Superior Bigrand Enormatrixul
* Bisuperior Enormatrixul, 200![200(2)200(2)200(2)200,200,200]
* Bisuperior Kiloenormatrixul, (200![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200]
* Bisuperior Megaenormatrixul, ((200![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200]
* Bisuperior Grand Enormatrixul, 200(![200(2)200(2)200(2)200,200,200])200![200(2)200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200,200,200])200(![200(2)200(2)200(2)200,200,200])2+1
* Bisuperior Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200,200,200])200(![200(2)200(2)200(2)200,200,200])3+1
* Bisuperior Bigrand Enormatrixul
* ''Quadeusus-godsgodgogle'', <nowiki>E100#{{{{#}}}}#100</nowiki>
* ''Humeengulus'', {10,10,100,4} & 10
* ''Blasphemorgulquad'', <nowiki>E100#{{{{{1}}}}}#100</nowiki>
* ''Gongulquideus'', {10,100,1,5} & 10
* Enormaquaxul, 200![200(2)200(2)200(2)200(2)200]
* Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200]
* Megaenormaquaxul, ((200![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200]
* Gigaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])4
* Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200![200(2)200(2)200(2)200(2)200]+1
* Grand Kiloenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])2+1
* Grand Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])3+1
* Grand Gigaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])4+1
* Bigrand Enormaquaxul
* Trigrand Enormaquaxul
* Superior Enormaquaxul, 200![200(2)200(2)200(2)200(2)200,200]
* Superior Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200(2)200,200]
* Superior Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])3
* Superior Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200![200(2)200(2)200(2)200(2)200,200]+1
* Superior Grand Kiloenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200(2)200,200])2+1
* Superior Grand Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200(2)200,200])3+1
* Superior Bigrand Enormaquaxul
* Bisuperior Enormaquaxul, 200![200(2)200(2)200(2)200(2)200,200,200]
* Bisuperior Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200(2)200,200,200]
* Bisuperior Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200,200])3
* Bisuperior Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200,200])200![200(2)200(2)200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormaquaxul
* Bisuperior Grand Megaenormaquaxul
* Bisuperior Bigrand Enormaquaxul
* ''Humowngulus'', {10,10,100,5} & 10
* ''Gongulsideus'', {10,100,1,6} & 10
* ''Humungulus'', {10,10,100,6} & 10
* Super Even More Godder Tritri, 3 [3 {3 <3 / 3> 3} 3] 3
* ''Generatrix'', {10,10,10,10} & 10
* ''Gorgonghoulgog'', E100*(#)100
* ''General gogulus'', E100{#,#,#,#}100
* ''Grand gorgonghoulgog'', E100*(#)100#2
* ''The gathering''
* ''Blasphemorgulus regiment|Howling gorgonghoulgog'', E100*(*(#))100
* ''Blasphemorgulus regiment|Howling howling gorgonghoulgog'', E100*(*(*(#)))100
* Trexommthet, <math>f_{\theta(\Omega^3,0)}(10)</math>
* Blasphemormegabackulus / mega blasphemorbackulus, {10,10[1[1\4¬2]2]2}
* ''Transmorgrifihgh'', E100*(*(...*(*(#))...))100 w/100 *'s ~ E100#/^#100
* Mega blasphemorgoogol, {100,100[1[1\4¬2]2]2}

=== Part 6.18: <math>f_{\varphi(1,0,0,0,0)}^2(10)</math> ~ <math>f_{\psi_0(\Omega^{\Omega^\omega})}^2(10)</math> ===
* ''Incridulus'', {10,10,10,100,2} & 10
* ''Incradulus'', {10,10,10,100,3} & 10
* ''Increedulus'', {10,10,10,100,4} & 10
* ''Incrowdulus'', {10,10,10,100,5} & 10
* ''Incrundulus'', {10,10,10,100,6} & 10
* ''Pendecatrix'', {10,10,10,10,10} & 10 = 5 & 10 & 10
* ''Tercredulus'', {10,10,10,10,100} & 10
* Quadrexommthet, <math>f_{\theta(\Omega^4,0)}(10)</math>
* ''Tercridulus'', {10,10,10,10,100,2} & 10
* ''Tercradulus'', {10,10,10,10,100,3} & 10
* ''Tercreedulus'', {10,10,10,10,100,4} & 10
* ''Tercrowdulus'', {10,10,10,10,100,5} & 10
* ''Hexdecatrix'', {10,10,10,10,10,10} & 10 = 6 & 10 & 10
* ''Pencredulus'', {10,10,10,10,10,100} & 10
* Quintexommthet, <math>f_{\theta(\Omega^5,0)}(10)</math>
* ''Pencridulus'', {10,10,10,10,10,100,2} & 10
* ''Pencradulus'', {10,10,10,10,10,100,3} & 10
* ''Pencreedulus'', {10,10,10,10,10,100,4} & 10
* ''Excredulus'', {10,10,10,10,10,10,100} & 10
* Sextexommthet, <math>f_{\theta(\Omega^6,0)}(10)</math>
* ''Excridulus'', {10,10,10,10,10,10,100,2} & 10
* ''Excradulus'', {10,10,10,10,10,10,100,3} & 10
* ''Excreedulus'', {10,10,10,10,10,10,100,4} & 10
* ''Epcredulus'', {10,10,10,10,10,10,10,100} & 10
* Septexommthet, <math>f_{\theta(\Omega^7,0)}(10)</math>
* ''Ogcredulus'', {10,10,10,10,10,10,10,10,100} & 10
* ''Lineatrix'', 10 & 10 & 10
* Octexommthet, <math>f_{\theta(\Omega^8,0)}(10)</math>
* ''Encredulus'', {10,10,10,10,10,10,10,10,10,100} & 10
* Demagoogol, {100,100[1[1\9¬2]2]2}
* ''Demagogue'', E100{#,10(1)2}100
* Nonexommthet, <math>f_{\theta(\Omega^9,0)}(10)</math>
* ''Decredulus'', {10,10,10,10,10,10,10,10,10,10,100} & 10
* Dekexommthet, <math>f_{\theta(\Omega^{10},0)}(10)</math>
* Small veblasphemorbackulus, {10,10[1[1\1,2¬2]2]2}
* Ominongoogol, {100,100[1[1\1,2¬2]2]2}
* ''Goobawamba'', <math>\{10,100 (1) 2\}\ \&\ 10</math>
* Small veblasphemorgoogol, {100,100[1[1\1,2¬2]2]2}
* Hektexommthet, <math>f_{\theta(\Omega^{100},0)}(10)</math>
* ''Ominongulus'', E100{#,100(1)2}100
* Destruxul, 200![200(200)200]
* Kilodestruxul, (200![200(200)200])![200(200)200]
* Megadestruxul, ((200![200(200)200])![200(200)200])![200(200)200]
* Gigadestruxul, (((200![200(200)200])![200(200)200])![200(200)200])![200(200)200]
* Teradestruxul, 200(![200(200)200])5
* Petadestruxul, 200(![200(200)200])6
* Exadestruxul, 200(![200(200)200])7
* Grand Destruxul, 200(![200(200)200])200![200(200)200]+1
* Grand Kilodestruxul, 200(![200(200)200])(200![200(200)200])![200(200)200]+1
* Grand Megadestruxul, 200(![200(200)200])((200![200(200)200])![200(200)200])![200(200)200]+1
* Grand Gigadestruxul, 200(![200(200)200])200(![200(200)200])4+1
* Grand Teradestruxul, 200(![200(200)200])200(![200(200)200])5+1
* Grand Petadestruxul, 200(![200(200)200])200(![200(200)200])6+1
* Grand Exadestruxul, 200(![200(200)200])200(![200(200)200])7+1
* Bigrand Destruxul, 200(![200(200)200])200(![200(200)200])200![200(200)200]+1+1
* Bigrand Kilodestruxul, 200(![200(200)200])200(![200(200)200])(200![200(200)200])![200(200)200]+1+1
* Bigrand Megadestruxul, 200(![200(200)200])200(![200(200)200])((200![200(200)200])![200(200)200])![200(200)200]+1+1
* Trigrand Destruxul, 200(![200(200)200])200(![200(200)200])200(![200(200)200])200![200(200)200]+1+1+1
* Trigrand Kilodestruxul
* Quadgrand Destruxul
* Quintgrand Destruxul
* Great Destruxul, 200![200(200)200(200)200]
* Great Kilodestruxul, (200![200(200)200(200)200])![200(200)200(200)200]
* Great Megadestruxul, ((200![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200]
* Great Gigadestruxul, (((200![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200]
* Great Grand Destruxul, 200(![200(200)200(200)200])200![200(200)200(200)200]+1
* Great Grand Kilodestruxul, 200(![200(200)200(200)200])(200![200(200)200(200)200])![200(200)200(200)200]+1
* Great Grand Megadestruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])3+1
* Great Grand Gigadestruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])4+1
* Great Bigrand Destruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])200![200(200)200(200)200]+1+1
* Great Trigrand Destruxul
* Bigreat Destruxul, 200![200(200)200(200)200(200)200]
* Bigreat Kilodestruxul, (200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Megadestruxul, ((200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Gigadestruxul, (((200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Grand Destruxul, 200(![200(200)200(200)200(200)200])200![200(200)200(200)200(200)200]+1
* Bigreat Grand Kilodestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])2+1
* Bigreat Grand Megadestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])3+1
* Bigreat Grand Gigadestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])4+1
* Bigreat Bigrand Destruxul
* Bigreat Trigrand Destruxul
* Võro, <math>f_{\psi_0(\Omega^{\Omega^\omega})}(420)</math> in the fast-growing hierarchy (using the extended Buchholz's function, ψ0(Ω^Ω^ω) denotes the small Veblen ordinal)
* Kilexommthet, <math>f_{\theta(\Omega^{1000},0)}(10)</math>
* Megexommthet, <math>f_{\theta(\Omega^{10^6},0)}(10)</math>
* ''Pseudomonarchia daemonum'', E100#{#,#(1)2}44,435,622
* Gigexommthet, <math>f_{\theta(\Omega^{10^9},0)}(10)</math>
* Terexommthet, <math>f_{\theta(\Omega^{10^{12}},0)}(10)</math>
* Petexommthet, <math>f_{\theta(\Omega^{10^{15}},0)}(10)</math>
* Exexommthet, <math>f_{\theta(\Omega^{10^{18}},0)}(10)</math>
* Zettexommthet, <math>f_{\theta(\Omega^{10^{21}},0)}(10)</math>
* Yottexommthet, <math>f_{\theta(\Omega^{10^{24}},0)}(10)</math>
* ''Dorsatrix'', <math>\{10,(10^{100}) (1) 2\}\ \&\ 10</math>
* ''Lineatrixplex'', {10,lineatrix(1)2} & 10

=== Part 6.19: <math>f_{\psi_0(\Omega^{\Omega^\omega})}^2(10)</math> ~ <math>f_{\psi_0(\Omega^{\Omega^\Omega})}^2(10)</math> ===
* ''Grand ominongulus'', E100{#,#(1)2}100#2
* ''Grangol-carta-ominongulus'', E100{#,#(1)2}100#100
* Bird's number, <math>\approx f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))</math>
* ''Godgahlah-carta-ominongulus'', E100{#,#(1)2}100#^#100
* ''Godsgodgulus-carta-ominongulus'', E100{#,#(1)2}100#{#}#100
* ''Ominongulus-by-deuteron'', E100{#,#(1)2}100{#,#(1)2}100
* ''Ominongulus-by-triton'', E100{#,#(1)2}100{#,#(1)2}100{#,#(1)2}100
* '''TREE sequence|TREE[3]''' (lower bound)
* Treegol (BlankEntity) (TREE[10100])
* Factoree, (TREE[200!] = TREE(7.88657867365 × 10374])
* Apple Tree (TREE[Apple])
* Fresh Xeno-Nobel-Multidimensional Stardust Onion from the future (TREE[gonion])
* Egg Salad (TREE[g{Egg,Egg(Egg,Egg)Egg,Egg}!1010100])
* Multiversoogol, {100,100[1[2\1,2¬2]2]2}
* Metaversoogol, {100,100[1[1\1,1,2¬2]1[1[3\2¬2]1[3\2¬2]1[3\2¬2]1[3\2¬2]2]2]2}
* ''Bixtendol'', s(3,3{1``2}2)
* Destrubixul, 200![200([200(200)200])200]
* Kilodestrubixul, (200![200([200(200)200])200])![200([200(200)200])200]
* Megadestrubixul, 200(![200([200(200)200])200])3
* Gigadestrubixul, 200(![200([200(200)200])200])4
* Grand Destrubixul, 200(![200([200(200)200])200])200![200([200(200)200])200]+1
* Grand Kilodestrubixul, 200(![200([200(200)200])200])(200![200([200(200)200])200])![200([200(200)200])200]+1
* Grand Megadestrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])3+1
* Grand Gigadestrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])4+1
* Bigrand Destrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])200![200([200(200)200])200]+1+1
* Trigrand Destrubixul
* Great Destrubixul, 200![200([200(200)200(200)200])200(200)200]
* Great Kilodestrubixul, 200(![200([200(200)200(200)200])200(200)200])2
* Great Megadestrubixul, 200(![200([200(200)200(200)200])200(200)200])3
* Great Grand Destrubixul
* Great Grand Kilodestrubixul
* Great Grand Megadestrubixul
* Great Bigrand Destrubixul
* Bigreat Destrubixul, 200![200([200(200)200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestrubixul, 200(![200([200(200)200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestrubixul, 200(![200([200(200)200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destrubixul
* Bigreat Grand Kilodestrubixul
* Bigreat Grand Megadestrubixul
* Bigreat Bigrand Destrubixul
* Destrutrixul, 200![200([200([200(200)200])200])200]
* Kilodestrutrixul, 200(![200([200([200(200)200])200])200])2
* Megadestrutrixul, 200(![200([200([200(200)200])200])200])3
* Gigadestrutrixul, 200(![200([200([200(200)200])200])200])4
* Grand Destrutrixul, 200(![200([200([200(200)200])200])200])200![200([200([200(200)200])200])200]+1
* Grand Kilodestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])2+1
* Grand Megadestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])3+1
* Grand Gigadestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])4+1
* Bigrand Destrutrixul
* Trigrand Destrutrixul
* Great Destrutrixul, 200![200([200([200(200)200(200)200])200(200)200])200(200)200]
* Great Kilodestrutrixul, 200(![200([200([200(200)200(200)200])200(200)200])200(200)200])2
* Great Megadestrutrixul, 200(![200([200([200(200)200(200)200])200(200)200])200(200)200])3
* Great Grand Destrutrixul
* Great Grand Kilodestrutrixul
* Great Grand Megadestrutrixul
* Great Bigrand Destrutrixul
* Bigreat Destrutrixul, 200![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestrutrixul, 200(![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestrutrixul, 200(![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destrutrixul
* Bigreat Grand Kilodestrutrixul
* Bigreat Grand Megadestrutrixul
* Bigreat Bigrand Destrutrixul
* Destruquaxul, 200![200([200([200([200(200)200])200])200])200]
* Kilodestruquaxul, 200(![200([200([200([200(200)200])200])200])200])2
* Megadestruquaxul, 200(![200([200([200([200(200)200])200])200])200])3
* Gigadestruquaxul, 200(![200([200([200([200(200)200])200])200])200])4
* Grand Destruquaxul, 200(![200([200([200([200(200)200])200])200])200])200![200([200([200([200(200)200])200])200])200]+1
* Grand Kilodestruquaxul
* Grand Megadestruquaxul
* Grand Gigadestruquaxul
* Bigrand Destruquaxul
* Trigrand Destruquaxul
* Great Destruquaxul, 200![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200]
* Great Kilodestruquaxul, 200(![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200])2
* Great Megadestruquaxul, 200(![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200])3
* Great Grand Destruquaxul
* Great Grand Kilodestruquaxul
* Great Grand Megadestruquaxul
* Great Bigrand Destruquaxul
* Bigreat Destruquaxul, 200![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestruquaxul, 200(![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestruquaxul, 200(![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destruquaxul
* Bigreat Grand Kilodestruquaxul
* Bigreat Grand Megadestruquaxul
* Bigreat Bigrand Destruquaxul
* Bitetrommthet, <math>f_{\theta(\Omega^\Omega,0)}(10)</math>
* ''Gibbawamba'', <math>\{10,100,2 (1) 2\}\ \&\ 10</math>
* Little birdie, {100,100[1[1\1\2¬2]2]2}
* Białystok, <math>f_{\psi_0(\Omega^{\Omega^{\Omega}})}(576)</math>

=== Part 6.20: <math>f_{\psi_0(\Omega^{\Omega^\Omega})}^2(10)</math> ~ <math>f_{\psi_0(\varepsilon_{\Omega+1})}^2(10)</math> ===
* ''Gabbawamba'', <math>\{10,100,3 (1) 2\}\ \&\ 10</math>
* ''Geebawamba'', <math>\{10,100,4 (1) 2\}\ \&\ 10</math>
* ''Gibawamba'', <math>\{10,100,5 (1) 2\}\ \&\ 10</math>
* ''Gobbawamba'', <math>\{10,100,6 (1) 2\}\ \&\ 10</math>
* ''Gabawamba'', <math>\{10,100,7 (1) 2\}\ \&\ 10</math>
* ''Boobawamba'', <math>\{10,10,100 (1) 2\}\ \&\ 10</math>
* ''Corporawamba'', <math>\{10,100,1,2 (1) 2\}\ \&\ 10</math>
* ''Mulporawamba'', <math>\{10,100,2,2 (1) 2\}\ \&\ 10</math>
* ''Powporawamba'', <math>\{10,100,3,2 (1) 2\}\ \&\ 10</math>
* ''Terporawamba'', <math>\{10,100,4,2 (1) 2\}\ \&\ 10</math>
* ''Pepporawamba'', <math>\{10,100,5,2 (1) 2\}\ \&\ 10</math>
* ''Hexporawamba'', <math>\{10,100,6,2 (1) 2\}\ \&\ 10</math>
* ''Bibbawamba'', <math>\{10,10,100,2 (1) 2\}\ \&\ 10</math>
* ''Corplodawamba'', <math>\{10,100,1,3 (1) 2\}\ \&\ 10</math>
* ''Babbawamba'', <math>\{10,10,100,3 (1) 2\}\ \&\ 10</math>
* ''Cordetawamba'', <math>\{10,100,1,4 (1) 2\}\ \&\ 10</math>
* ''Beebawamba'', <math>\{10,10,100,4 (1) 2\}\ \&\ 10</math>
* ''Bibawamba'', <math>\{10,10,100,5 (1) 2\}\ \&\ 10</math>
* ''Bobbawamba'', <math>\{10,10,100,6 (1) 2\}\ \&\ 10</math>
* ''Babawamba'', <math>\{10,10,100,7 (1) 2\}\ \&\ 10</math>
* ''Troobawamba'', <math>\{10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Tribbawamba'', <math>\{10,10,10,100,2 (1) 2\}\ \&\ 10</math>
* ''Trabbawamba'', <math>\{10,10,10,100,3 (1) 2\}\ \&\ 10</math>
* ''Treebawamba'', <math>\{10,10,10,100,4 (1) 2\}\ \&\ 10</math>
* ''Quadroobawamba'', <math>\{10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Quintoobawamba'', <math>\{10,10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Sextoobawamba'', <math>\{10,10,10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Goobawantra'', <math>\{10,100 (1) 3\}\ \&\ 10</math>
* ''Gibbawantra'', <math>\{10,100,2 (1) 3\}\ \&\ 10</math>
* ''Gabbawantra'', <math>\{10,100,3 (1) 3\}\ \&\ 10</math>
* ''Geebawantra'', <math>\{10,100,4 (1) 3\}\ \&\ 10</math>
* ''Gibawantra'', <math>\{10,100,5 (1) 3\}\ \&\ 10</math>
* ''Gobbawantra'', <math>\{10,100,6 (1) 3\}\ \&\ 10</math>
* ''Gabawantra'', <math>\{10,100,7 (1) 3\}\ \&\ 10</math>
* ''Boobawantra'', <math>\{10,10,100 (1) 3\}\ \&\ 10</math>
* ''Troobawantra'', <math>\{10,10,10,100 (1) 3\}\ \&\ 10</math>
* ''Quadroobawantra'', <math>\{10,10,10,10,100 (1) 3\}\ \&\ 10</math>
* ''Goobawanquadra'', <math>\{10,100 (1) 4\}\ \&\ 10</math>
* ''Boobawanquadra'', <math>\{10,10,100 (1) 4\}\ \&\ 10</math>
* ''Troobawanquadra'', <math>\{10,10,10,100 (1) 4\}\ \&\ 10</math>
* ''Goobawanquinta'', <math>\{10,100 (1) 5\}\ \&\ 10</math>
* ''Emperatrix'', <math>\{10,10 (1) 10\}\ \&\ 10</math>
* ''Gossablossla'', <math>\{10,10 (1) 100\}\ \&\ 10</math>
* ''Hecatonchirechelon'', E100{#,#(1)#}100
* ''Gissablossla'', <math>\{10,10 (1) 100,2\}\ \&\ 10</math>
* ''Gassablossla'', <math>\{10,10 (1) 100,3\}\ \&\ 10</math>
* ''Geesablossla'', <math>\{10,10 (1) 100,4\}\ \&\ 10</math>
* ''Gussablossla'', <math>\{10,10 (1) 100,5\}\ \&\ 10</math>
* ''Hyperlatrix'', <math>\{10,10 (1) 10,10\}\ \&\ 10</math>
* ''Mossablossla'', <math>\{10,10 (1) 10,100\}\ \&\ 10</math>
* ''Missablossla'', <math>\{10,10 (1) 10,100,2\}\ \&\ 10</math>
* ''Massablossla'', <math>\{10,10 (1) 10,100,3\}\ \&\ 10</math>
* ''Meesablossla'', <math>\{10,10 (1) 10,100,4\}\ \&\ 10</math>
* ''Mussablossla'', <math>\{10,10 (1) 10,100,5\}\ \&\ 10</math>
* ''Bossablossla'', <math>\{10,10 (1) 10,10,100\}\ \&\ 10</math>
* ''Bissablossla'', <math>\{10,10 (1) 10,10,100,2\}\ \&\ 10</math>
* ''Bassablossla'', <math>\{10,10 (1) 10,10,100,3\}\ \&\ 10</math>
* ''Beesablossla'', <math>\{10,10 (1) 10,10,100,4\}\ \&\ 10</math>
* ''Trossablossla'', <math>\{10,10 (1) 10,10,10,100\}\ \&\ 10</math>
* ''Quadrossablossla'', <math>\{10,10 (1) 10,10,10,10,100\}\ \&\ 10</math>
* ''Quintossablossla'', <math>\{10,10 (1) 10,10,10,10,10,100\}\ \&\ 10</math>
* ''Sextossablossla'', <math>\{10,10 (1) 10,10,10,10,10,10,100\}\ \&\ 10</math>
* ''Diteratrix'', <math>\{10,10 (1)(1) 2\}\ \&\ 10</math>
* ''Goobaduamba'', <math>\{10,100 (1)(1) 2\}\ \&\ 10</math>
* ''Gibbaduamba'', <math>\{10,100,2 (1)(1) 2\}\ \&\ 10</math>
* ''Goobaduantra'', <math>\{10,100 (1)(1) 3\}\ \&\ 10</math>
* ''Goobaduanquadra'', <math>\{10,100 (1)(1) 4\}\ \&\ 10</math>
* ''Admiratrix'', <math>\{10,10 (1)(1) 10\}\ \&\ 10</math>
* ''Dutridecatrix'', <math>\{10,3 (2) 2\}\ \&\ 10</math>
* Mega Super Even More Godder Tritri, 3 [3 {3 <3 / 3 / 3> 3} 3] 3
* ''Triteratrix'', <math>\{10,10 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobatriombia'', <math>\{10,100 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobatriontria'', <math>\{10,100 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobaquardimbia'', <math>\{10,100 (1)(1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobaquindingia'', <math>\{10,100 (1)(1)(1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobasesixtia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{6\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobasebiptia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{7\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobagogdiktia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{8\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobanogdiktia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{9\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Xaplorgulus'', <math>\{10,10 (2) 2\}\ \&\ 10</math>
* ''Goobadektimtia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{10\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goxxogogulus'', E100{100x100&#}100
* ''Goxxablorg'', <math>\{10,100 (2) 2\}\ \&\ 10</math>
* ''Gixxablorg'', <math>\{10,100,2 (2) 2\}\ \&\ 10</math>
* ''Gaxxablorg'', <math>\{10,100,2 (2) 2\}\ \&\ 10</math>
* ''Boxxablorg'', <math>\{10,10,100 (2) 2\}\ \&\ 10</math>
* ''Troxxablorg'', <math>\{10,10,10,100 (2) 2\}\ \&\ 10</math>
* ''Grand xaplorgulus'', <math>\{10,10 (2) 3\}\ \&\ 10</math>
* ''Gooxadworg'', <math>\{10,100 (2)(2) 2\}\ \&\ 10</math>
* ''Goxxathrorg'', <math>\{10,100 (2)(2)(2) 2\}\ \&\ 10</math>
* ''Goxxaquorg'', <math>\{10,100 (2)(2)(2)(2) 2\}\ \&\ 10</math>
* ''Cosslorgulus'', <math>\{10,10 (3) 2\}\ \&\ 10</math>
* ''Cloxxogogulus'', E100{100x100x100&#}100
* ''Coxxablorg'', <math>\{10,100 (3) 2\}\ \&\ 10</math>
* ''Coxxadworg'', <math>\{10,100 (3)(3) 2\}\ \&\ 10</math>
* ''Coxxathrorg'', <math>\{10,100 (3)(3)(3) 2\}\ \&\ 10</math>
* ''Coxxaquorg'', <math>\{10,100 (3)(3)(3)(3) 2\}\ \&\ 10</math>
* ''Tesslorgulus'', <math>\{10,10 (4) 2\}\ \&\ 10</math>
* ''Teroxxogogulus'', E100{100^4&#}100
* ''Toxxablorg'', <math>\{10,100 (4) 2\}\ \&\ 10</math>
* ''Pesslorgulus'', <math>\{10,10 (5) 2\}\ \&\ 10</math>
* ''Poxxablorg'', <math>\{10,100 (5) 2\}\ \&\ 10</math>
* ''Hesslorgulus'', <math>\{10,10 (6) 2\}\ \&\ 10</math>
* ''Hexxablorg'', <math>\{10,100 (6) 2\}\ \&\ 10</math>
* ''Zesslorgulus'', <math>\{10,10 (7) 2\}\ \&\ 10</math>
* ''Zexxablorg'', <math>\{10,100 (7) 2\}\ \&\ 10</math>
* ''Yosslorgulus'', <math>\{10,10 (8) 2\}\ \&\ 10</math>
* ''Yoxxablorg'', <math>\{10,100 (8) 2\}\ \&\ 10</math>
* ''Brosslorgulus'', <math>\{10,10 (9) 2\}\ \&\ 10</math>
* ''Broxxablorg'', <math>\{10,100 (9) 2\}\ \&\ 10</math>
* ''Gosslorgulus'', <math>\{10,10 (10) 2\}\ \&\ 10</math>
* ''Gexxablorg'', <math>\{10,100 (10) 2\}\ \&\ 10</math>
* ''Cosmatrix'', <math>\{10,10 (10) 10\}\ \&\ 10</math>
* ''Mosslorgulus'', <math>\{10,10 (20) 2\}\ \&\ 10</math>
* ''Hasslorgulus'', <math>\{10,10 (30) 2\}\ \&\ 10</math>
* ''Kysslorgulus'', <math>\{10,10 (40) 2\}\ \&\ 10</math>
* ''Pisslorgulus'', <math>\{10,10 (50) 2\}\ \&\ 10</math>
* ''Sasslorgulus'', <math>\{10,10 (60) 2\}\ \&\ 10</math>
* ''Pexxlorgulus'', <math>\{10,10 (70) 2\}\ \&\ 10</math>
* ''Nisslorgulus'', <math>\{10,10 (80) 2\}\ \&\ 10</math>
* ''Zozzlorgulus'', <math>\{10,10 (90) 2\}\ \&\ 10</math>
* ''Golapulus'' / Alphlorgulus, <math>\{10,10 (100) 2\}\ \&\ 10</math>
* ''Brobdingnagongule'', E100{100^100&#}100
* ''Besslorgulus'', <math>\{10,10 (200) 2\}\ \&\ 10</math>
* ''Gasslorgulus'', <math>\{10,10 (300) 2\}\ \&\ 10</math>
* ''Desslorgulus'', <math>\{10,10 (400) 2\}\ \&\ 10</math>
* Zitrite, <math>f_{\psi_0(\Omega^{\Omega^{\Omega^\omega}})}(420)</math> in the fast-growing hierarchy (using the extended Buchholz's function)
* ''Thesslorgulus'', <math>\{10,10 (500) 2\}\ \&\ 10</math>
* ''Iottlorgulus'', <math>\{10,10 (600) 2\}\ \&\ 10</math>
* ''Kapplorgulus'', <math>\{10,10 (700) 2\}\ \&\ 10</math>
* ''Lasslorgulus'', <math>\{10,10 (800) 2\}\ \&\ 10</math>
* ''Sigglorgulus'', <math>\{10,10 (900) 2\}\ \&\ 10</math>
* Tritetrommthet, <math>f_{\theta(\Omega^{\Omega^\Omega},0)}(10)</math>
* ''Ginglapulus'', <math>\{10,100 (0,2) 2\}\ \&\ 10</math>
* Belgorod, <math>f_{\psi_0(\Omega^{\Omega^{\Omega^{\Omega}}})}(576) = f_{\psi_0(\psi_{1}^5(0))}(576)</math> in the fast-growing hierarchy (using the extended Buchholz's function)
* ''Ganglapulus'', <math>\{10,100 (0,3) 2\}\ \&\ 10</math>
* ''Geenglapulus'', <math>\{10,100 (0,4) 2\}\ \&\ 10</math>
* ''Gownglapulus'', <math>\{10,100 (0,5) 2\}\ \&\ 10</math>
* ''Gunglapulus'', <math>\{10,100 (0,6) 2\}\ \&\ 10</math>
* ''Bolapulus'', <math>\{10,100 (0,0,1) 2\}\ \&\ 10</math>
* ''Binglapulus'', <math>\{10,100 (0,0,2) 2\}\ \&\ 10</math>
* ''Banglapulus'', <math>\{10,100 (0,0,3) 2\}\ \&\ 10</math>
* ''Beenglapulus'', <math>\{10,100 (0,0,4) 2\}\ \&\ 10</math>
* ''Trolapulus'', <math>\{10,100 (0,0,0,1) 2\}\ \&\ 10</math>
* ''Tringlapulus'', <math>\{10,100 (0,0,0,2) 2\}\ \&\ 10</math>
* ''Tranglapulus'', <math>\{10,100 (0,0,0,3) 2\}\ \&\ 10</math>
* ''Quadrolapulus'', <math>\{10,100 (0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Quadringlapulus'', <math>\{10,100 (0,0,0,0,2) 2\}\ \&\ 10</math>
* ''Quintolapulus'', <math>\{10,100 (0,0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Sextolapulus'', <math>\{10,100 (0,0,0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Goplapulus'' / ''Centolapulus'', <math>\{10,100 ((1)1) 2\}\ \&\ 10</math>
* Quadritetrommthet, <math>f_{\theta(\Omega^{\Omega^{\Omega^\Omega}},0)}(10)</math>
* ''Goplapulusfact'', <math>\{10,100 (1(1)1) 2\}\ \&\ 10</math>
* ''Gogridplapulus'', <math>\{10,100 (2(1)1) 2\}\ \&\ 10</math>
* ''Gokubikplapulus'', <math>\{10,100 (3(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulplapulus'', <math>\{10,100 (0,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulplapulusfact'', <math>\{10,100 (1,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolagridpulplapulus'', <math>\{10,100 (2,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolakubikpulplapulus'', <math>\{10,100 (3,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulusdeusplapulus'', <math>\{10,100 (0,2(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulustruceplapulus'', <math>\{10,100 (0,3(1)1) 2\}\ \&\ 10</math>
* ''Gobolapulplapulus'', <math>\{10,100 (0,0,1(1)1) 2\}\ \&\ 10</math>
* ''Gotrolapulplapulus'', <math>\{10,100 (0,0,0,1(1)1) 2\}\ \&\ 10</math>
* ''Goplapulusdeus'', <math>\{10,100 ((1)2) 2\}\ \&\ 10</math>
* ''Goplapulustruce'', <math>\{10,100 ((1)3) 2\}\ \&\ 10</math>
* ''Hyper-golapulusfact'', <math>\{10,100 ((1)0,1) 2\}\ \&\ 10</math>
* ''Hyper-ginglapulusfact'', <math>\{10,100 ((1)0,2) 2\}\ \&\ 10</math>
* ''Hyper-ganglapulusfact'', <math>\{10,100 ((1)0,3) 2\}\ \&\ 10</math>
* ''Hyper-bolapulusfact'', <math>\{10,100 ((1)0,0,1) 2\}\ \&\ 10</math>
* ''Hyper-trolapulusfact'', <math>\{10,100 ((1)0,0,0,1) 2\}\ \&\ 10</math>
* ''Giplapulus'', <math>\{10,100 ((1)(1)1) 2\}\ \&\ 10</math>
* ''Gaplapulus'', <math>\{10,100 ((1)(1)(1)1) 2\}\ \&\ 10</math>
* ''Geeplapulus'', <math>\{10,100 ((1)(1)(1)(1)1) 2\}\ \&\ 10</math>
* ''Boplapulus'', <math>\{10,100 ((2)1) 2\}\ \&\ 10</math>
* ''Biplapulus'', <math>\{10,100 ((2)(2)1) 2\}\ \&\ 10</math>
* ''Troplapulus'', <math>\{10,100 ((3)1) 2\}\ \&\ 10</math>
* ''Quadroplapulus'', <math>\{10,100 ((4)1) 2\}\ \&\ 10</math>
* ''Goduplapulus'', <math>\{10,100 ((0,1)1) 2\}\ \&\ 10</math>
* Quintitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow5,0)}(10)</math>
* ''Giduplapulus'', <math>\{10,100 ((0,2)1) 2\}\ \&\ 10</math>
* ''Boduplapulus'', <math>\{10,100 ((0,0,1)1) 2\}\ \&\ 10</math>
* ''Gotriplapulus'', <math>\{10,100 (((1)1)1) 2\}\ \&\ 10</math>
* Sextitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow6,0)}(10)</math>
* ''Goquadriplapulus'', <math>\{10,100 (((0,1)1)1) 2\}\ \&\ 10</math>
* Septitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow7,0)}(10)</math>
* ''Goquintiplapulus'', <math>\{10,100 ((((1)1)1)1) 2\}\ \&\ 10</math>
* Octitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow8,0)}(10)</math>
* Nonitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow9,0)}(10)</math>
* Dekotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10,0)}(10)</math>
* ''Lugubrigoth'', E100{#^^#&#}100
* Lugubrigoogol, {100,100[1[1¬3]2]2}
* ''Quathragoth/goplatoth'', <math>10\uparrow\uparrow100 \& 10 \& 10</math>
* Hektotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow100,0)}(10)</math>
* Extremexul, 200![1(1)[2200,200,200,200
* Extremedollaxul, 200$0]3]
* Kiloextremexul, (200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200
* Megaextremexul, ((200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200)![1(1)[2200,200,200,200
* Gigaextremexul, 200(![1(1)[2200,200,200,200)4
* Teraextremexul, 200(![1(1)[2200,200,200,200)5
* Petaextremexul, 200(![1(1)[2200,200,200,200)6
* Exaextremexul, 200(![1(1)[2200,200,200,200)7
* Grand Extremexul, 200(![1(1)[2200,200,200,200)200![1(1)[2200,200,200,200+1
* Grand Kiloextremexul, 200(![1(1)[2200,200,200,200)(200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200+1
* Grand Megaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)3+1
* Grand Gigaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)4+1
* Grand Teraextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)5+1
* Grand Petaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)6+1
* Grand Exaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)7+1
* Bigrand Extremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)200![1(1)[2200,200,200,200+1+1
* Bigrand Kiloextremexul
* Bigrand Megaextremexul
* Trigrand Extremexul
* Trigrand Kiloextremexul
* Trigrand Megaextremexul
* Quadgrand Extremexul
* Quintgrand Extremexul
* Kilotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow1000,0)}(10)</math>
* Megotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^6,0)}(10)</math>
* Gigotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^9,0)}(10)</math>
* Terotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{12},0)}(10)</math>
* Petotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{15},0)}(10)</math>
* Exotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{18},0)}(10)</math>
* Zettotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{21},0)}(10)</math>
* Yottotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{24},0)}(10)</math>

== Higher computable level ==

=== Part 6.21: <math>f_{\psi_0(\Omega_2)}^2(10)</math> ~ <math>f_{\psi_0(\Omega_\omega)}^2(10)</math> ===

* Trugubrigoogol, {100,100[1[1¬4]2]2}
* Omega Mega Super Even More Godder Tritri, 3 [3 {3 // 3} 3] 3
* Tetrugubrigoogol, {100,100[1[1¬5]2]2}
* Pentugubrigoogol, {100,100[1[1¬6]2]2}
* Hexugubrigoogol, {100,100[1[1¬7]2]2}
* Heptugubrigoogol, {100,100[1[1¬8]2]2}
* Ogdugubrigoogol, {100,100[1[1¬9]2]2}
* Ennugubrigoogol, {100,100[1[1¬10]2]2}
* Dekugubrigoogol, {100,100[1[1¬11]2]2}
* Centugubrigoogol, {100,100[1[1¬1,2]2]2}
* Big Bird, <math>\{100,100 [1 [1 \neg 1 \neg 2] 2] 2\}</math>
* Extremebixul, 200![1(1)[2200,200,200,200,200
* Kiloextremebixul, (200![1(1)[2200,200,200,200,200)![1(1)[2200,200,200,200,200
* Extremetrixul, 200![1(1)[2200,200,200,200,200,200
* Extremequaxul, 200![1(1)[2200,200,200,200,200,200,200
* Tria-hierarchaxis, {100,100[1[1[2\32]2]2]2}
* Bommthet, <math>f_{\theta(\Omega_2,0)}(10)</math>
* Gigantixul, 200![1(1)[3200,200,200
* Gigantibixul, 200![1(1)[3200,200,200,200
* Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 /// 3} 3] 3
* Gigantitrixul, 200![1(1)[3200,200,200,200,200
* Gigantiquaxul, 200![1(1)[3200,200,200,200,200,200
* Tetra-hierarchaxis, {100,100[1[1[1[2\42]2]2]2]2}
* Trommthet, <math>f_{\theta(\Omega_3,0)}(10)</math>
* Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 <<<3 <<<3 /// 3>>> 3>>> 3} 3] 3
* Penta-hierarchaxis, {100,100[1[1[1[1[2\52]2]2]2]2]2}
* Quadrommthet, <math>f_{\theta(\Omega_4,0)}(10)</math>
* Hexa-hierarchaxis, {100,100[1[1[1[1[1[2\62]2]2]2]2]2]2}
* Quintommthet, <math>f_{\theta(\Omega_5,0)}(10)</math>
* Hepta-hierarchaxis, {100,100[1[1[1[1[1[1[2\72]2]2]2]2]2]2]2}
* Sextommthet, <math>f_{\theta(\Omega_6,0)}(10)</math>
* Octa-hierarchaxis, {100,100[1[1[1[1[1[1[1[2\82]2]2]2]2]2]2]2]2}
* Septommthet, <math>f_{\theta(\Omega_7,0)}(10)</math>
* Enna-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[2\92]2]2]2]2]2]2]2]2]2}
* Octommthet, <math>f_{\theta(\Omega_8,0)}(10)</math>
* Deka-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[1[2\102]2]2]2]2]2]2]2]2]2]2}
* Nonommthet, <math>f_{\theta(\Omega_9,0)}(10)</math>
* Dekommthet, <math>f_{\theta(\Omega_{10},0)}(10)</math>
* Corporalmax / hecta-hierarchaxis, {100,100[1[2\1,22]2]2}
* Hektommthet, <math>f_{\theta(\Omega_{100},0)}(10)</math>
* Kilommthet, <math>f_{\theta(\Omega_{1000},0)}(10)</math>
* Megommthet, <math>f_{\theta(\Omega_{10^6},0)}(10)</math>
* Gigommthet, <math>f_{\theta(\Omega_{10^9},0)}(10)</math>
* Terommthet, <math>f_{\theta(\Omega_{10^{12}},0)}(10)</math>
* Petommthet, <math>f_{\theta(\Omega_{10^{15}},0)}(10)</math>
* Exommthet, <math>f_{\theta(\Omega_{10^{18}},0)}(10)</math>
* Zettommthet, <math>f_{\theta(\Omega_{10^{21}},0)}(10)</math>
* Yottommthet, <math>f_{\theta(\Omega_{10^{24}},0)}(10)</math>
* '''SCG(13)''' (lower bound), <math>\approx f_{\psi(\Omega_\omega)}(13)</math>
* QZAZARZ (ɧ51), TREE(G64*(TREE(SCG(13))) + 1
* LoveDeath, SCG1521(7)
* ''Meeting point of the three hierarchies'', <math>f_{\theta(\Omega_{\omega})}(100)</math>
* Nucleabixul, 200![[200200]200]

=== Part 6.22: <math>f_{\psi_0(\Omega_\omega)}^2(10)</math> ~ <math>f_{\psi_0(\Phi(1,0))+1}(10)</math> ===

* Pair sequence number, <math>\approx f_{\psi(\Omega_\omega)+1}(10)</math>
* Stage array notation|Stage array number, <math>\approx f_{\psi(\Omega_{\omega})+1}(100)</math>
* Mulporalmax, {100,100[1[1[2\2,22]2]2]2}
* Big Chunk, {10,100 [1 [1 [1 \2,2 3] 2] 2] 2}
* Powporalmax, {100,100[1[1[1[2\3,22]2]2]2]2}
* Corplodalmax, {100,100[1[1[2\1,32]2]2]2}
* Absolutely Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 \ 3, 3} 3] 3
* Cordetalmax, {100,100[1[1[1[2\1,42]2]2]2]2}
* Meg-Googolmax, {100,100[1[2\1,1,22]2]2}
* Dumeg-Googolmax, {100,100[1[1[2\1,1,32]2]2]2}
* Gig-Googolmax, {100,100[1[2\1,1,1,22]2]2}
* Dugig-Googolmax, {100,100[1[1[2\1,1,1,32]2]2]2}
* Ter-Googolmax, {100,100[1[2\1,1,1,1,22]2]2}
* Goobolmax, {100,100[1[2\1[2]22]2]2}
* Gibbolmax, {100,100[1[1[2\2[2]22]2]2]2}
* Gootrolmax, {100,100[1[1[2\1[2]32]2]2]2}
* Gooterolmax, {100,100[1[1[1[2\1[2]42]2]2]2]2}
* Diteralmax / dubolmax, {100,100[1[2\1[2]1[2]22]2]2}
* Xappolmax, {100,100[1[2\1[3]22]2]2}
* Colossolmax, {100,100[1[2\1[4]22]2]2}
* Goplexulusmax, {100,100[1[2\1[1[2]2]22]2]2}
* Bimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega)})}(10)</math>
* Tethrinoogolmax, {100,100[1[2\1[1\2]22]2]2}
* Tethrinoofactimax / hecto-tethrinoogolmax, {100,100[1[2\1[2\2]22]2]2}
* Terrible tethrinoogolmax, {100,100[1[2\1[1\3]22]2]2}
* Terrible terrible tethrinoogolmax, {100,100[1[2\1[1\4]22]2]2}
* Tethrinoocrossmax, {100,100[1[2\1[1\1\2]22]2]2}
* Secundotethrated-tethrinoocrossmax, {100,100[1[2\1[1\1\3]22]2]2}
* Tethrinoocubormax, {100,100[1[2\1[1\1\1\2]22]2]2}
* Tethrinooteronmax, {100,100[1[2\1[1\1\1\1\2]22]2]2}
* Tethrinootopemax, {100,100[1[2\1[1[2\22]2]22]2]2}
* Mountommol, {100,100[1[2\1[1[2\32]2]22]2]2}
* Mountobbol, {100,100[1[2\1[1[2\42]2]22]2]2}
* Mountotrtrol, {100,100[1[2\1[1[2\52]2]22]2]2}
* Mountoquadquadol, {100,100[1[2\1[1[2\62]2]22]2]2}
* Mountoquinquinol, {100,100[1[2\1[1[2\72]2]22]2]2}
* Mountosextsextol, {100,100[1[2\1[1[2\82]2]22]2]2}
* Mountoseptseptol, {100,100[1[2\1[1[2\92]2]22]2]2}
* Mountooctoctol, {100,100[1[2\1[1[2\102]2]22]2]2}
* Mountononnonol, {100,100[1[2\1[1[2\112]2]22]2]2}
* Dimen-Mountommol, {100,100[1[2\1[1[2\122]2]22]2]2}
* Mountimmol, {100,100[1[2\1[1[2\1,22]2]22]2]2}
* Trimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})}(10)</math>
* Quadrimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})}(10)</math>
* Quintimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})})}(10)</math>
* Sextimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{6\ \Omega's}}(10)</math>
* Septimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{7\ \Omega's}}(10)</math>
* Octimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{8\ \Omega's}}(10)</math>
* Nonimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{9\ \Omega's}}(10)</math>
* Dekomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10\ \Omega's}}(10)</math>
* Hektomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{100\ \Omega's}}(10)</math>
* Kilomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{1000\ \Omega's}}(10)</math>
* Megomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^6\ \Omega's}}(10)</math>
* Gigomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^9\ \Omega's}}(10)</math>
* Teromixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{12}\ \Omega's}}(10)</math>
* Petomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{15}\ \Omega's}}(10)</math>
* Exomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{18}\ \Omega's}}(10)</math>
* Zettomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{21}\ \Omega's}}(10)</math>
* Yottomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{24}\ \Omega's}}(10)</math>
* Binommwil, <math>f_{\psi(\Omega_\Omega)}(10)</math>
* The HUS, S(U(H(3)))
* Grand HUS, S(S(S(U(U(U(H(H(H(3)))))))))
* Great HUS, S(S(S( ... (S(U(U(U( ... (U(H(H(H( ... (H(3))) ... ))) (with the HUS number of S's, the HUS number of U's, and the HUS number of H's)
* Nucleatrixul, 200![[[200200]200]200]
* Trinommwil, <math>f_{\psi(\Omega_{\Omega_\Omega})}(10)</math>
* Nucleaquaxul, 200![[[[200200]200]200]200]
* Quadrinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_\Omega}})}(10)</math>
* Quintinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_\Omega}}})}(10)</math>
* Sextinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_{\Omega_\Omega}}}})}(10)</math>
* Septinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{7\ \Omega's})}(10)</math>
* Octinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{8\ \Omega's})}(10)</math>
* Noninommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{9\ \Omega's})}(10)</math>
* Dekinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10\ \Omega's})}(10)</math>
* Kilinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{1000\ \Omega's})}(10)</math>
* Meginommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^6\ \Omega's})}(10)</math>
* Giginommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^9\ \Omega's})}(10)</math>
* Terinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{12}\ \Omega's})}(10)</math>
* Petinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{15}\ \Omega's})}(10)</math>
* Exinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{18}\ \Omega's})}(10)</math>
* Zettinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{21}\ \Omega's})}(10)</math>
* Yottinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{24}\ \Omega's})}(10)</math>

=== Part 6.23: <math>> f_{\psi_0(\Phi_1(0))+1}(10)</math> ===

* Unimah, <math>f_{\psi(I)}(10)</math>
* Bitetrotos, <math>f_{\psi(I^I)}(10)</math>
* Tritetrotos, <math>f_{\psi(I^{I^I})}(10)</math>
* Quadritetrotos, <math>f_{\psi(I^{I^{I^I}})}(10)</math>
* Quintitetrotos, <math>f_{\psi(I^{I^{I^{I^I}}})}(10)</math>
* Sextitetrotos, <math>f_{\psi(I\uparrow\uparrow6)}(10)</math>
* Septitetrotos, <math>f_{\psi(I\uparrow\uparrow7)}(10)</math>
* Octitetrotos, <math>f_{\psi(I\uparrow\uparrow8)}(10)</math>
* Nonitetrotos, <math>f_{\psi(I\uparrow\uparrow9)}(10)</math>
* Dekotetrotos, <math>f_{\psi(I\uparrow\uparrow10)}(10)</math>
* Hektotetrotos, <math>f_{\psi(I\uparrow\uparrow100)}(10)</math>
* Kilotetrotos, <math>f_{\psi(I\uparrow\uparrow1000)}(10)</math>
* Megotetrotos, <math>f_{\psi(I\uparrow\uparrow10^6)}(10)</math>
* Gigotetrotos, <math>f_{\psi(I\uparrow\uparrow10^9)}(10)</math>
* Terotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{12})}(10)</math>
* Petotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{15})}(10)</math>
* Exotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{18})}(10)</math>
* Zettotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{21})}(10)</math>
* Yottotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{24})}(10)</math>
* Uninotos, <math>f_{\psi(I_I)}(10)</math>
* Binotos, <math>f_{\psi(I_{I_I})}(10)</math>
* Trinotos, <math>f_{\psi(I_{I_{I_I}})}(10)</math>
* Sextinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{7\ I's})}(10)</math>
* Dekinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{11\ I's})}(10)</math>
* Hektinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{101\ I's})}(10)</math>
* Kilinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{1001\ I's})}(10)</math>
* Meginotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^6+1\ I's})}(10)</math>
* Giginotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^9+1\ I's})}(10)</math>
* Terinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{12}+1\ I's})}(10)</math>
* Petinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{15}+1\ I's})}(10)</math>
* Exinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{18}+1\ I's})}(10)</math>
* Zettinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{21}+1\ I's})}(10)</math>
* Yottinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{24}+1\ I's})}(10)</math>
* KumaKuma ψ function#Large Function and Large Number|Kumakuma 3 variables ψ number, F10100(10100)
* Bimah, <math>f_{\psi(I(2,0))}(10)</math>
* Trimah, <math>f_{\psi(I(3,0))}(10)</math>
* Quadrimah, <math>f_{\psi(I(4,0))}(10)</math>
* Quintimah, <math>f_{\psi(I(5,0))}(10)</math>
* Sextimah, <math>f_{\psi(I(6,0))}(10)</math>
* Septimah, <math>f_{\psi(I(7,0))}(10)</math>
* Octimah, <math>f_{\psi(I(8,0))}(10)</math>
* Nonimah, <math>f_{\psi(I(9,0))}(10)</math>
* Dekimah, <math>f_{\psi(I(10,0))}(10)</math>
* Hektimah, <math>f_{\psi(I(100,0))}(10)</math>
* Kilimah, <math>f_{\psi(I(1000,0))}(10)</math>
* Megimah, <math>f_{\psi(I(10^6,0))}(10)</math>
* Gigimah, <math>f_{\psi(I(10^9,0))}(10)</math>
* Terimah, <math>f_{\psi(I(10^{12},0))}(10)</math>
* Petimah, <math>f_{\psi(I(10^{15},0))}(10)</math>
* Eximah, <math>f_{\psi(I(10^{18},0))}(10)</math>
* Zettimah, <math>f_{\psi(I(10^{21},0))}(10)</math>
* Yottimah, <math>f_{\psi(I(10^{24},0))}(10)</math>
* Uninimah, <math>f_{\psi(I(I(0,0),0))}(10)</math>
* Binimah, <math>f_{\psi(I(I(I(0,0),0),0))}(10)</math>
* Trinimah, <math>f_{\psi(I(I(I(I(0,0),0),0),0))}(10)</math>
* Quadrinimah, <math>f_{\psi(I(I(I(I(I(0,0),0),0),0),0))}(10)</math>
* Quintinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{6\ I's})}(10)</math>
* Sextinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{7\ I's})}(10)</math>
* Septinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{8\ I's})}(10)</math>
* Terinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{12}+1\ I's})}(10)</math>
* Zettinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{21}+1\ I's})}(10)</math>
* Yottinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{24}+1\ I's})}(10)</math>
* ε function#Large Number|グラハム数ver ε.0.1.0 (Graham's number version ε.0.1.0), G64(4)
* Tritetremar, <math>f_{\psi(M^{M^M})}(10)</math>
* Sextitetremar, <math>f_{\psi(M\uparrow\uparrow6)}(10)</math>
* Terotetremar, <math>f_{\psi(M\uparrow\uparrow10^{12})}(10)</math>
* Petotetremar, <math>f_{\psi(M\uparrow\uparrow10^{15})}(10)</math>
* Exotetremar, <math>f_{\psi(M\uparrow\uparrow10^{18})}(10)</math>
* Zettotetremar, <math>f_{\psi(M\uparrow\uparrow10^{21})}(10)</math>
* Yottotetremar, <math>f_{\psi(M\uparrow\uparrow10^{24})}(10)</math>
* Uninemar, <math>f_{\psi(M_M)}(10)</math>
* Trinemar, <math>f_{\psi(M_{M_{M_M}})}(10)</math>
* Quadrinemar, <math>f_{\psi(M_{M_{M_{M_M}}})}(10)</math>
* Quintinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{6\ M's})}(10)</math>
* Sextinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{7\ M's})}(10)</math>
* Kilinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{1001\ M's})}(10)</math>
* Meginemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^6+1\ M's})}(10)</math>
* Giginemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^9+1\ M's})}(10)</math>
* Petinemar|TTerinemar|erinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{12}+1\ M's})}(10)</math>
* Petinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{15}+1\ M's})}(10)</math>
* Exinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{18}+1\ M's})}(10)</math>
* Zettinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{21}+1\ M's})}(10)</math>
* Yottinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{24}+1\ M's})}(10)</math>
* Uninamus, <math>f_{\psi(M(M(0;0);0))}(10)</math>
* Meginamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{6}+1\ M's})}(10)</math>
* Exinamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{18}+1\ M's})}(10)</math>
* Yottinamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{24}+1\ M's})}(10)</math>
* SAN number, ~ (0,0,0)(1,1,1)(2,2,1)(3,0,0)(0,0,0)[64]
* Tritar, <math>f_{C(C(C(\Omega_{3}2,0),0),0)}(3) = Tar(3)</math>
* Quadritar, <math>f_{C(C(C(C(\Omega_{4}2,0),0),0),0)}(4) = Tar(4)</math>
* Quintitar, <math>f_{C(C(C(C(C(\Omega_{5}2,0),0),0),0),0)}(5) = Tar(5)</math>
* Sextitar, <math>f_{C(C(C(C(C(C(\Omega_{6}2,0),0),0),0),0),0)}(6) = Tar(6)</math>
* Septitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{7}2,0),0),\cdots ),0)}_{7\text{ C's}}}(7) = Tar(7)</math>
* Octitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{8}2,0),0),\cdots ),0)}_{8\text{ C's}}}(8) = Tar(8)</math>
* Nonitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{9}2,0),0),\cdots ),0)}_{9\text{ C's}}}(9) = Tar(9)</math>
* Dekotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10}2,0),0),\cdots ),0)}_{10\text{ C's}}}(10) = Tar(10)</math>
* Hektotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{100}2,0),0),\cdots ),0)}_{100\text{ C's}}}(100) = Tar(100)</math>
* Kilotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{1000}2,0),0),\cdots ),0)}_{1000\text{ C's}}}(1000) = Tar(1000)</math>
* Megotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{6}}2,0),0),\cdots ),0)}_{10^{6}\text{ C's}}}(10^{6}) = Tar(10^{6})</math>
* Gigotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{9}}2,0),0),\cdots ),0)}_{10^{9}\text{ C's}}}(10^{9}) = Tar(10^{9})</math>
* Terotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{12}}2,0),0),\cdots ),0)}_{10^{12}\text{ C's}}}(10^{12}) = Tar(10^{12})</math>
* Petotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{15}}2,0),0),\cdots ),0)}_{10^{15}\text{ C's}}}(10^{15}) = Tar(10^{15})</math>
* Exotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{18}}2,0),0),\cdots ),0)}_{10^{18}\text{ C's}}}(10^{18}) = Tar(10^{18})</math>
* Zettotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{21}}2,0),0),\cdots ),0)}_{10^{21}\text{ C's}}}(10^{21}) = Tar(10^{21})</math>
* Yottotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{24}}2,0),0),\cdots ),0)}_{10^{24}\text{ C's}}}(10^{24}) = Tar(10^{24})</math>
* Ronnotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{27}}2,0),0),\cdots ),0)}_{10^{27}\text{ C's}}}(10^{27}) = Tar(10^{27})</math>
* Quettotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{30}}2,0),0),\cdots ),0)}_{10^{30}\text{ C's}}}(10^{30}) = Tar(10^{30})</math>
* Unintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Dekotar}}2,0),0),\cdots ),0)}_{\text{Dekotar C's}}}(\text{Dekotar}) = Tar(Dekotar) = Tar(Tar)</math>
* Bintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Unintar}}2,0),0),\cdots ),0)}_{\text{Unintar C's}}}(\text{Unintar}) = Tar(Tar(Tar)) = Tar(Tar(Dekotar))</math>
* Trintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Bintar}}2,0),0),\cdots ),0)}_{\text{Bintar C's}}}(\text{Bintar}) = Tar(Tar(Tar(Tar)))</math>
* Quadrintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{3\text{-intar}}2,0),0),\cdots ),0)}_{3\text{-intar C's}}}(3\text{-intar}) = Tar^{4}(Tar)</math>
* Quintintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{4\text{-intar}}2,0),0),\cdots ),0)}_{4\text{-intar C's}}}(4\text{-intar}) = Tar^{5}(Tar)</math>
* Sextintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{5\text{-intar}}2,0),0),\cdots ),0)}_{5\text{-intar C's}}}(5\text{-intar}) = Tar^{6}(Tar)</math>
* Septintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{6\text{-intar}}2,0),0),\cdots ),0)}_{6\text{-intar C's}}}(6\text{-intar}) = Tar^{7}(Tar)</math>
* Octintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{7\text{-intar}}2,0),0),\cdots ),0)}_{7\text{-intar C's}}}(7\text{-intar}) = Tar^{8}(Tar)</math>
* Nonintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{8\text{-intar}}2,0),0),\cdots ),0)}_{8\text{-intar C's}}}(8\text{-intar}) = Tar^{9}(Tar)</math>
* Dekintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{9\text{-intar}}2,0),0),\cdots ),0)}_{9\text{-intar C's}}}(9\text{-intar}) = Tar^{10}(Tar)</math>
* Hektintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{99\text{-intar}}2,0),0),\cdots ),0)}_{99\text{-intar C's}}}(99\text{-intar}) = Tar^{100}(Tar)</math>
* Kilintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{999\text{-intar}}2,0),0),\cdots ),0)}_{999\text{-intar C's}}}(999\text{-intar}) = Tar^{1000}(Tar)</math>
* Megintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{6}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{6}-1)\text{-intar C's}}}((10^{6}-1)\text{-intar}) = Tar^{10^{6}}(Tar)</math>
* Gigintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{9}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{9}-1)\text{-intar C's}}}((10^{9}-1)\text{-intar}) = Tar^{10^{9}}(Tar)</math>
* Terintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{12}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{12}-1)\text{-intar C's}}}((10^{12}-1)\text{-intar}) = Tar^{10^{12}}(Tar)</math>
* Petintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{15}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{15}-1)\text{-intar C's}}}((10^{15}-1)\text{-intar}) = Tar^{10^{15}}(Tar)</math>
* Exintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{18}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{18}-1)\text{-intar C's}}}((10^{18}-1)\text{-intar}) = Tar^{10^{18}}(Tar)</math>
* Zettintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{21}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{21}-1)\text{-intar C's}}}((10^{21}-1)\text{-intar}) = Tar^{10^{21}}(Tar)</math>
* Yottintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{24}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{24}-1)\text{-intar C's}}}((10^{24}-1)\text{-intar}) = Tar^{10^{24}}(Tar)</math>
* When the death metal music prevail to Armenian toddlers under five in certain isolated areas and cultural divisions during the clash
* Tarintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(Dekotar-1)\text{-intar}}2,0),0),\cdots ),0)}_{(Dekotar-1)\text{-intar C's}}}((Dekotar-1)\text{-intar}) = Tar^{Tar}(Tar)</math>
* '''[[Loader 数|Loader's number]]''' (output of loader.c), <math>D^5(99)</math>
* Stained Ouija, <math>D^{1729}(10)</math>
* Bashicu matrix number with respect to Bashicu matrix system version 2.3
* ６ (N primitive)
* [[Y序列|Y sequence]] number, <math>f^{2000}(1)</math>
* <math>\omega-Y</math> sequence number, <math>f^{2000}(1)</math> using <math>f(n) = \omega-Y\ (1,\omega)[n]</math>

【[[Googolism - Part 5|更小]] | [[Googolism|主页]] | 更大】

[[分类:经典大数]]

用户:Baixie01000a7

2026-02-22T09:14:39Z

Baixie01000a7：

拜谢

<chem>CO2 + C -> 2 CO</chem>

<math>\mathrm{Ciallo}\sim(\angle\cdot\omega<)\frown\bigstar</math>

DEN

2026-02-22T08:53:06Z

Baixie01000a7：重定向页面至iblp

#REDIRECT [[iblp]]

Y序列 VS TBMS

2026-02-21T09:53:15Z

Baixie01000a7：重定向页面至Y 序列 vs TBMS

#REDIRECT [[Y_序列_vs_TBMS]]

用户:Baixie01000a7/TON草稿

2026-02-20T13:53:06Z

Baixie01000a7：创建页面，内容为“Taranovsky 序数记号 (Taranovsky’s ordinal notation, TON) 是 Taranovsky 提出的一系列记号的总称。无反射配置的情况下，TON 具有如下的版本： * 反射度：Degrees of Reflection (DR)。 * 包含通过的自下而上：Built-from-below with Passthrough (BP)。 * 包含通过的反射度：Degrees of Reflection with Passthrough (DRP)。 * 主要序数体系：Main Ordinal Notation System (M)。 * 主要序数体系（通过扩展…”

Taranovsky 序数记号 (Taranovsky’s ordinal notation, TON) 是 Taranovsky 提出的一系列记号的总称。

无反射配置的情况下，TON 具有如下的版本：

* 反射度：Degrees of Reflection (DR)。
* 包含通过的自下而上：Built-from-below with Passthrough (BP)。
* 包含通过的反射度：Degrees of Reflection with Passthrough (DRP)。
* 主要序数体系：Main Ordinal Notation System (M)。
* 主要序数体系（通过扩展）：Main ordinal notation system (Passthrough extension)(MP)。
* ''n'' 自下而上迭代（无 4b 版本）：Iteration of ''n''-built from below (variation without 4b)(I)。
* ''n'' 自下而上迭代：Iteration of ''n''-built from below (IBP)。
* ''n'' 自下而上迭代（通过扩展）：Iteration of ''n''-built from below (Passthrough extension)(IP)。

有反射配置的情况下，TON 具有如下的版本：

* 反射配置版反射度：Reflection configuration version of Degrees of Reflection (DRC)。
* 反射配置版包含通过的反射度：Reflection configuration version of Degrees of Reflection with Passthrough (DRPC)。
* 反射配置版主要序数记号体系：Reflection configuration version of Main Ordinal Notation System (MC)。
* 反射配置版主要序数记号体系（通过扩展）：Reflection configuration version of Main ordinal notation system (Passthrough extension) (MPC)。

=== 共同定义 ===
大多数记号都是使用两个常数和一个函数构建的。常数包括 <math>0</math> ，以及 <math>\Omega</math> 或 <math>\Omega_n</math> 之一（其

中 ''n'' 是系统内的给定自然数）。函数通常用 ''C'' 表示，是二元的。

# <math>0</math> 或和 <math>\Omega</math> （或 <math>\Omega_n</math> ）是项。
# 如果 a 和 ''b'' 是项，则C(a,b)是项。

项可以用“''>''”、“''<''”或“=”进行比较和连接。

首先，以后缀形式写出项，即删除所有“(”、“)”和“'',''”，然后反转字符串。其次，按

字典序比较后缀形式，其中<math>C</math> < <math>0</math> < <math>\Omega</math> （或 <math>\Omega_n</math> 为最大单个字母）。

在体系之中，只有一部分项是标准的。

常数是标准的。

如果以下 3 项全部为真，则是标准的。

# a 和 b 都是标准的。
# 如果 b = C(c, d)，则 a ≤ c。
# 此条件在各个不同的体系之间有所不同，通常称之为“自下而上条件”。

要检查“自下而上条件”，我们需要检查 a 的语法树。在定义中：

# 量词不是在项上，而是在 a 内的位置上，因此不同位置的相同项会得到不同的处理。
# <math>x \sqsubseteq y</math> 表示 x 是 y 的子项（也是 <math>x \sqsupseteq y</math> ）。使用位置索引（例如，<math>C(C(C(C(C(\Omega, 0), C(\Omega, \Omega)), 0), 0)</math>中的三个 0 位于位置 (1, 1, 1, 2),(1, 2) 和 (2)），y 的位置索引是 x 的位置索引的初始子串。
# x <math>x \sqsubset y</math> y 表示 x 是 y 的真子项（也是 y <math>x \sqsupset y</math> x ）。即<math>x\subseteq y \wedge x \neq y</math>。

一个标准项表示一个序数，不同的标准项表示不同的序数。序数的序关系被定义为标准项的序关系。

因此，最小标准项 0 对应于最小序数 0 。大于 b1, b2, · · · 的标准项 a 对应于大于 b1, b2, · · ·对应的序数。

这些定义并不能确保良定义，因此需要证明。目前，只有一个体系被充分证明是良定义的。

Taranovsky 记号具有如下共同的性质：

1. <math>C(a,b)>b</math>。

2. <math>C(a,b)</math>在a和b上都是单调的，在a上是连续的。

3. <math>C(a,b)=b+\omega^{a}</math>当且仅当C(a,b)≥a。

第三个性质可以帮助我们进行标准项和 [[康托范式|Cantor 标准形式]] (CNF) 之间的转换。

由于 Ω是一个“大”序数，使得ωΩ= Ω，因此也可以在标准项和基数为 Ω 的 CNF 之间进行转换。

自下而上的条件是不同系统的不同之处。它由 3 个不同的概念组合而成：自下而上方法、通过和反射配置。自下而上方法最先引入，然后是通过，最后是反射配置。因此，这三个概念构成了 TON 的三代。

BSM

2026-02-20T13:30:30Z

Baixie01000a7：

Bashicu急矩阵(Bashicu Sudden Matrix,BSM)是Bashicu Hyudora发明的序数记号。它目前还未被证明[[良序]]。它被认为是[[急模式]]的源头。

== 定义 ==
''前排提示：请先阅读[[BMS]]和[[BHM]]的定义''

BSM只有找坏根规则和BMS不一致。以下介绍不一致的地方。

# 第0列：默认行、列标均从1开始，并在第1列之前加上一个额外的没有值的第0列。如果BHM中一个元素没有父项，则取其父项为同行第0列的元素。
# '''子项'''：如果项A的父项是项B，则称A是B的子项。
# '''待定坏根'''：待定坏根为末列最靠下的非0项(LNZ)的'''所有祖先项'''（包括第0列元素）的子项所在列。特别的，如果末列最下非0项不在第1行，则要求待定坏根正上方的元素应当是末列最下非0项正上方的元素的祖先项。我们称待定根集合中的一些根为“小根”，一些根为“大根”。大根与小根是不冲突的，这意味着，一个根可能既不是小根也不是大根，也可能同时是小根和大根。坏根的选择，和小根与大根息息相关。
# '''预展开'''：根据找到的待定坏根r，确定待定好部G'，待定坏部B'，末列L，待定阶差向量<math>\Delta'</math>，随后'''按照BMS的规则'''得到r对应的预展开式<math>S_r=G'\sim B'\sim (B'+\Delta') \sim (L+\Delta')</math>(其中~是序列连接)。特别的，我们称最右侧的待定坏根（即BMS意义的坏根）对应的预展开式为基准式。
# '''小根'''：至少满足下列两条件之一的根r是小根：①r的预展开式在字典序上小于基准式。②如果根r是最右侧待定坏根的祖先项，且第r列和最右侧待定坏根所处列的第t+1行到最后一行，'''不能完全对应相同'''(t是LNZ所处行号)。
# '''大根'''：如果根r是最右侧待定坏根的祖先项，且满足第r列和最右侧待定坏根所处列的第t+1行到最后一行，'''完全对应相同'''
#坏根：坏根定义为在所有“是小根但不是大根”的待定坏根右边的第一个待定坏根。特别的，如果不存在这样的这样的待定坏根，则坏根是最左侧待定坏根。

BSM的极限基本列是<math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),\cdots\}</math>,因此从这里面的元素经过不断取基本列或取前驱所能得到的式子是BSM的标准式，否则不是标准式。

值得注意的是，单行BSM又称急序列(Sudden Sequence System,'''SSS'''),也是一个很有名的[[序数记号]]。

实例：

例1：<math>(0)(1)(2)</math>

可以发现LNZ的祖先是第0项、第1项、第2项。找到它们的所有子项，是第1项和第2项。于是给出预展开式<math>S_1=(0)(1)(1)(2)(3)</math>,<math>S_2=(0)(1)(1)(2)</math>.因此小根是第0项。因此坏根是第1项。得到展开式是<math>(0)(1)(1)(2)(2)(3)(3)(4)\cdots</math>.

例2：<math>(0,0)(1,1)(2,0)(3,1)(3,0)</math>

我们用红色标记其待定坏根：<math>({\color{red}0},0)({\color{red}1},1)({\color{red}2},0)(3,1)(3,0)</math>,前两个待定坏根均为最右侧待定坏根第三列第一行的2的祖先项，第一列第一行的0下方的元素和最右侧待定坏根下方的元素完全一致，因此它是一个大根。而第二列第一行的1下方的元素和最右侧待定坏根下方的元素不一致，因此它是一个小根。在这里我们很幸运，可以直接得出坏根是第三列第一行的2.于是展开式是<math>(0,0)(1,1)(2,0)(3,1)(2,0)(3,1)(2,0)(3,1)\cdots</math>

例3：<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)</math>

我们用红色标记其待定坏根：<math>({\color{red}0},0)({\color{red}1},1)({\color{red}1},0)({\color{red}1},0)({\color{red}2},0)(3,1)(3,0)</math>.其中第一列第一行的0和第四列第一行的1是最右侧待定坏根2的祖先项。可以发现它们都是大根。接下来是各个待定坏根的预展开式：<math>S_5=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)(3,0)</math>,它是基准式。接下来有<math>S_4=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(4,1)(4,0)</math>然后是<math>S_3=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,0)(4,1)(4,0)</math>。然后是<math>S_2=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,1)(2,0)(2,0)(3,0)(4,1)(4,0)</math>.然后是<math>S_1=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(5,0)</math>.比较字典序后发现，第二列第一行的1、第三列第一行的1、第四列第一行的1的预展开式都大于基准式，因此它们都不是小根。但因为第一列第一行的0和第四列第一行的1是大根，因此坏根是第四列第一行的1.于是得到展开式<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(4,1)\cdots</math>

== 枚举和强度分析 ==
参见词条[[BSM分析]]

{{默认排序:序数记号}}
[[分类:记号]]

用户:Baixie01000a7

2026-02-20T13:26:04Z

Baixie01000a7：

拜谢

<chem>CO2 + C -> 2 CO</chem>

用户:Baixie01000a7

2026-02-20T13:25:35Z

Baixie01000a7：创建页面，内容为“拜谢”

拜谢

DcN

2026-02-20T12:25:23Z

Baixie01000a7：

DcN，是 318`4 创造的便于打字的记号，主要用于写 FOS 中作为序数的项，几乎不可能良定义，主要通过枚举列表来主观推算定义。DcN 的极限是 <math>\varphi(10,0)</math>，Y_cpper 将其扩展到 <math>\Gamma_0</math>，现在一般在 <math>\varphi(\omega,0)</math> 之后使用这个扩展。DcN 的所有符号都集中在电脑键盘左上方的一小片区域，qwerty13456789，456789 使用频率很低，Veblen 记号需要随时要输入括号下标希腊字母，1-Y 则有比 DcN 更长的常见表达式，所以 DcN 便于打字，是专为 FOS 中常见序数设计的记号；但因为可读性差，DcN 一直没能流传开来。

因为完全无r的 DcN 存在歧义，比如 wtw1wtww 可以是 <math>\omega^{\omega^2}+\omega^\omega</math>，也可以是 <math>\omega^{\omega^{\omega^2}+\omega}</math>，因此在表达 FOS 的项时，建议使用含 r 的 DcN，但是去掉所有位于表达式末尾的 r，如 <math>\omega^{\omega^{\omega^\omega}}</math>=wtwtwtwrrr 记作 wtwtwtw。

1-Y 不必多说，是 Yukito 在 2019 年创造的序列记号，首次引入山脉图，在 Y(1,3) 之前有非常优秀的性质，因此也常用于表达 FOS 中作为项的序数。不过为简便，写 1-Y 表达式时通常省略 Y( ) 外壳和逗号，超过 10 的数字用拉丁字母表示，超过 36 则无写法。

在研究 FOS 的定义、构造原理时，使用 1-Y 的情况更多，因为 1-Y 的山脉结构和 FOS 中项内部的山脉结构类似；而在研究 FOS 的分析、强度形成原理时，为简便起见，使用 DcN 更多。在阅读 FOS 的枚举列表之前，请务必将本文的枚举列表熟透于心中，否则用 Veblen 记号或 OCF 写 FOS 表达式费时费力。
{| class="wikitable"
|-
!序数（十进制 + Cantor 记号 + Veblen 记号）
!DcN
!1-Y
|-
|<math>0</math>
|0
|<math>\varnothing</math>
|-
|<math>1</math>
|1
|1
|-
|<math>2</math>
|11
|11
|-
|<math>3</math>
|111
|111
|-
|<math>\omega</math>
|w
|12
|-
|<math>\omega+1</math>
|1w
|121
|-
|<math>\omega+2</math>
|11w
|1211
|-
|<math>\omega2</math>
|w1
|1212
|-
|<math>\omega2+1</math>
|1w1
|12121
|-
|<math>\omega3</math>
|w11
|121212
|-
|<math>\omega3+1</math>
|1w11
|1212121
|-
|<math>\omega^2</math>
|ww
|122
|-
|<math>\omega^2+1</math>
|1ww
|1221
|-
|<math>\omega^2+\omega</math>
|w1ww
|12212
|-
|<math>\omega^2+\omega+1</math>
|1w1ww
|122121
|-
|<math>\omega^2+\omega2</math>
|w11ww
|1221212
|-
|<math>\omega^2+\omega2+1</math>
|1w11ww
|12212121
|-
|<math>\omega^2+\omega3</math>
|w111ww
|122121212
|-
|<math>\omega^22</math>
|ww1
|122122
|-
|<math>\omega^22+\omega</math>
|w1ww1
|12212212
|-
|<math>\omega^22+\omega2</math>
|w11ww1
|1221221212
|-
|<math>\omega^23</math>
|ww11
|122122122
|-
|<math>\omega^3</math>
|www
|1222
|-
|<math>\omega^3+\omega</math>
|w1www
|122212
|-
|<math>\omega^3+\omega^2</math>
|ww1www
|1222122
|-
|<math>\omega^3+\omega^2+1</math>
|1ww1www
|12221221
|-
|<math>\omega^3+\omega^2+\omega</math>
|w1ww1www
|122212212
|-
|<math>\omega^3+\omega^2+\omega+1</math>
|1w1ww1www
|1222122121
|-
|<math>\omega^3+\omega^2+\omega2</math>
|w11ww1www
|12221221212
|-
|<math>\omega^3+\omega^22+\omega</math>
|w1ww11www
|122212212212
|-
|<math>\omega^3+\omega^22+\omega2+1</math>
|1w11ww11www
|122212212212121
|-
|<math>\omega^32</math>
|www1
|12221222
|-
|<math>\omega^4</math>
|wwww
|12222
|-
|<math>\omega^5</math>
|wwwww
|122222
|-
|<math>\omega^\omega</math>
|wtw
|123
|-
|<math>\omega^\omega+1</math>
|1wtw
|1231
|-
|<math>\omega^\omega+\omega</math>
|w1wtw
|12312
|-
|<math>\omega^\omega+\omega2</math>
|w11wtw
|1231212
|-
|<math>\omega^\omega+\omega^2</math>
|ww1wtw
|123122
|-
|<math>\omega^\omega2</math>
|w1tw
|123123
|-
|<math>\omega^\omega2+\omega^2</math>
|ww1w1tw
|123123122
|-
|<math>\omega^\omega3</math>
|w11tw
|123123123
|-
|<math>\omega^{\omega+1}</math>
|wt1w
|1232
|-
|<math>\omega^{\omega+1}+\omega^2</math>
|ww1wt1w
|1232122
|-
|<math>\omega^{\omega+1}+\omega^\omega</math>
|wtwr1wt1w
|1232123
|-
|<math>\omega^{\omega+1}+\omega^\omega2</math>
|w1twr1wt1w
|1232123123
|-
|<math>\omega^{\omega+1}2+\omega^\omega</math>
|wtwr1w1t1w
|12321232123
|-
|<math>\omega^{\omega+1}2+\omega^\omega2</math>
|w1twr1w1t1w
|12321232123123
|-
|<math>\omega^{\omega+1}3</math>
|w11t1w
|123212321232
|-
|<math>\omega^{\omega+2}</math>
|wt11w
|12322
|-
|<math>\omega^{\omega+3}</math>
|wt111w
|123222
|-
|<math>\omega^{\omega2}</math>
|wtw1
|12323
|-
|<math>\omega^{\omega2+1}</math>
|wt1w1
|123232
|-
|<math>\omega^{\omega2+1}+\omega^{\omega2}</math>
|wtw1r1wt1w1
|12323212323
|-
|<math>\omega^{\omega2+1}+\omega^{\omega2}2</math>
|w1tw1r1wt1w1
|1232321232312323
|-
|<math>\omega^{\omega2+1}2+\omega^{\omega2}2</math>
|w1tw1r1w1t1w1
|1232321232321232312323
|-
|<math>\omega^{\omega2+1}2+\omega^{\omega2}2+\omega^{\omega+1}2+\omega^{\omega}2</math>
|w1twr1w1t1wr1w1tw1r1w1t1w1
|123232123232123231232312321232123123
|-
|<math>\omega^{\omega2+2}</math>
|wt11w1
|1232322
|-
|<math>\omega^{\omega2+2}+\omega^{\omega2+1}</math>
|wt1w1r1wt11w1
|1232322123232
|-
|<math>\omega^{\omega3}</math>
|wtw11
|1232323
|-
|<math>\omega^{\omega3+1}+\omega^{\omega3}</math>
|wtw11r1wt1w11
|123232321232323
|-
|<math>\omega^{\omega4}</math>
|wtw111
|123232323
|-
|<math>\omega^{\omega^2}</math>
|wtww
|1233
|-
|<math>\omega^{\omega^2+\omega+1}+\omega^{\omega^2+\omega}</math>
|wtw1wwr1wt1w1ww
|1233232123323
|-
|<math>\omega^{\omega^22}</math>
|wtww1
|1233233
|-
|<math>\omega^{\omega^3}</math>
|wtwww
|12333
|-
|<math>\omega^{\omega^\omega}</math>
|wtwtw
|1234
|-
|<math>\omega^{\omega^{\omega2+1}3}</math>
|wtw11t1w1
|1234343234343234343
|-
|<math>\omega^{\omega^{\omega2+2}}</math>
|wtwt11w1
|12343433
|-
|<math>\omega^{\omega^{\omega3}}</math>
|wtwtw11
|12343434
|-
|<math>\omega^{\omega^{\omega^2}}</math>
|wtwtww
|12344
|-
|<math>\omega^{\omega^{\omega^\omega}}</math>
|wtwtwtw
|12345
|-
|<math>\varepsilon_0</math>
|e
|124
|-
|<math>\varepsilon_0+\omega</math>
|w1e
|12412
|-
|<math>\varepsilon_0+\omega^\omega</math>
|wtwr1e
|124123
|-
|<math>\varepsilon_02</math>
|e1
|124124
|-
|<math>\varepsilon_02+\omega</math>
|w1e1
|12412412
|-
|<math>\varepsilon_0\omega=\omega^{\varepsilon_0+1}</math>
|wt1e
|1242
|-
|<math>\omega^{\varepsilon_0+1}+\varepsilon_0</math>
|e1wt1e
|1242124
|-
|<math>\omega^{\varepsilon_0+1}2</math>
|w1t1e
|12421242
|-
|<math>\omega^{\varepsilon_0+2}</math>
|wt11e
|12422
|-
|<math>\omega^{\varepsilon_0+\omega}</math>
|wtw1e
|12423
|-
|<math>\omega^{\varepsilon_0+\omega^\omega}</math>
|wtwtwr1e
|124234
|-
|<math>\omega^{\varepsilon_02}</math>
|wte1
|12424
|-
|<math>\omega^{\omega^{\varepsilon_0+1}}</math>
|wtwt1e
|1243
|-
|<math>\omega^{\omega^{\varepsilon_0 2}}</math>
|wtwte1
|12435
|-
|<math>\varepsilon_1</math>
|ee
|1244
|-
|<math>\omega^{\varepsilon_12}</math>
|wtee1
|1244244
|-
|<math>\varepsilon_2</math>
|eee
|12444
|-
|<math>\varepsilon_\omega</math>
|etw
|1245
|-
|<math>\varepsilon_\omega+\omega^\omega</math>
|wtwr1etw
|1245123
|-
|<math>\varepsilon_\omega+\varepsilon_0</math>
|e1etw
|1245124
|-
|<math>\varepsilon_\omega2</math>
|e1tw
|12451245
|-
|<math>\omega^{\varepsilon_\omega+1}</math>
|wt1etw
|12452
|-
|<math>\omega^{\varepsilon_\omega+\omega}</math>
|wtw1etw
|124523
|-
|<math>\omega^{\varepsilon_\omega2}</math>
|wte1tw
|1245245
|-
|<math>\varepsilon_{\omega+1}</math>
|et1w
|12454
|-
|<math>\varepsilon_{\omega2}</math>
|etw1
|124545
|-
|<math>\varepsilon_{\omega^\omega}</math>
|etwtw
|12456
|-
|<math>\varepsilon_{\varepsilon_0}</math>
|ete
|12457
|-
|<math>\varepsilon_{\varepsilon_0+1}</math>
|et1e
|12457
|-
|<math>\varepsilon_{\varepsilon_1}</math>
|etee
|12457
|-
|<math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
|etete
|124578A
|-
|<math>\zeta_0</math>
|y
|1246
|-
|<math>\zeta_0+\varepsilon_0</math>
|e1y
|1246124
|-
|<math>\zeta_0+\varepsilon_{\varepsilon_0}</math>
|eter1y
|124612457
|-
|<math>\zeta_02</math>
|y1
|12461246
|-
|<math>\omega^{\zeta_0+1}</math>
|wt1y
|12462
|-
|<math>\omega^{\zeta_0+\varepsilon_\omega}</math>
|wtetwr1y
|1246245
|-
|<math>\omega^{\zeta_02}</math>
|wty1
|1246246
|-
|<math>\varepsilon_{\zeta_0+1}</math>
|ye=et1y
|12464
|-
|<math>\omega^{\varepsilon_{\zeta_0+1}+1}</math>
|wt1ye=wt1et1y
|124642
|-
|<math>\varepsilon_{\zeta_0+2}</math>
|yee=et11y
|124644
|-
|<math>\varepsilon_{\zeta_0+3}</math>
|yeee=et111y
|1246444
|-
|<math>\varepsilon_{\zeta_0+\omega}</math>
|etw1y
|124645
|-
|<math>\varepsilon_{\zeta_0+\omega^\omega}</math>
|etwtwr1y
|1246456
|-
|<math>\varepsilon_{\zeta_0+\varepsilon_0}</math>
|ete1y
|1246457
|-
|<math>\varepsilon_{\zeta_02}</math>
|ety1
|12464579
|-
|<math>\varepsilon_{\zeta_02+1}</math>
|et1y1
|124645794
|-
|<math>\varepsilon_{\zeta_03}</math>
|ety11
|124645794579
|-
|<math>\varepsilon_{\omega^{\zeta_0+1}}</math>
|etwt1y
|124645795
|-
|<math>\varepsilon_{\varepsilon_{\zeta_0+1}}</math>
|etet1y
|124645797
|-
|<math>\zeta_1</math>
|yy
|124646
|-
|<math>\varepsilon_{\zeta_1+1}</math>
|et1yy=yye
|1246464
|-
|<math>\zeta_2</math>
|yyy
|12464646
|-
|<math>\zeta_{\omega}</math>
|ytw
|12465
|-
|<math>\omega^{\zeta_{\omega}2}</math>
|wty1tw
|124652465
|-
|<math>\varepsilon_{\zeta_{\omega}+1}</math>
|et1ytw
|124654
|-
|<math>\varepsilon_{\zeta_{\omega}+\omega^{\varepsilon_0+1}}</math>
|etwt1er1ytw
|124654575
|-
|<math>\varepsilon_{\zeta_{\omega}+\varepsilon_\omega}</math>
|etetwr1ytw
|124654578
|-
|<math>\varepsilon_{\zeta_{\omega}+\zeta_0}</math>
|ety1ytw
|124654579
|-
|<math>\varepsilon_{\varepsilon_{\zeta_{\omega}2}}</math>
|etety1tw
|124654579878ACB
|-
|<math>\zeta_{\omega+1}</math>
|yt1w
|1246546
|-
|<math>\zeta_{\omega2}</math>
|ytw1
|124655
|-
|<math>\zeta_{\varepsilon_0}</math>
|yte
|124657
|-
|<math>\zeta_{\zeta_0}</math>
|yty
|1246579
|-
|<math>\eta_0</math>
|3
|12466
|-
|<math>\omega^{\eta_0+1}</math>
|wt13
|124662
|-
|<math>\omega^{\eta_0+\varepsilon_0}</math>
|wte13
|1246624
|-
|<math>\omega^{\eta_0+\zeta_0}</math>
|wty13
|12466246
|-
|<math>\omega^{\eta_02}</math>
|wt31
|124662466
|-
|<math>\varepsilon_{\eta_0+1}</math>
|3e=et13
|124664
|-
|<math>\varepsilon_{\eta_0+\omega}</math>
|etw13
|1246645
|-
|<math>\varepsilon_{\eta_0+\varepsilon_0}</math>
|ete13
|12466457
|-
|<math>\varepsilon_{\eta_0+\zeta_0}</math>
|ety13
|124664579
|-
|<math>\varepsilon_{\eta_02}</math>
|et31
|1246645799
|-
|<math>\zeta_{\eta_0+1}</math>
|3y=yt13
|1246646
|-
|<math>\zeta_{\eta_0+\omega}</math>
|ytw13
|12466465
|-
|<math>\zeta_{\eta_0+\varepsilon_0}</math>
|yte13
|124664657
|-
|<math>\zeta_{\eta_0+\zeta_0}</math>
|yty13
|1246646579
|-
|<math>\zeta_{\eta_02}</math>
|yt31
|12466465799
|-
|<math>\eta_1</math>
|33
|12466466
|-
|<math>\eta_\omega</math>
|3tw
|124665
|-
|<math>\eta_{\eta_0}</math>
|3t3
|124665799
|-
|<math>\varphi(4,0)</math>
|4
|124666
|-
|<math>\omega^{\varphi(4,0)2}</math>
|wt41
|1246662466
|-
|<math>\varepsilon_{\varphi(4,0)+1}</math>
|et41
|12466645799
|-
|<math>\zeta_{\varphi(4,0)+1}</math>
|yt41
|124666465799
|-
|<math>\eta_{\varphi(4,0)+1}</math>
|3t41
|1246664665799
|-
|<math>\varphi(4,1)</math>
|44
|1246664666
|-
|<math>\varphi(5,0)</math>
|5
|1246666
|-
|<math>\varphi(6,0)</math>
|6
|12466666
|-
|<math>\varphi(7,0)</math>
|7
|124666666
|-
|<math>\varphi(8,0)</math>
|8
|1246666666
|-
|<math>\varphi(4,\varphi(8,0)+1)+\eta_0</math>
|3184=314t18
|1246666666466657999999912466
|-
|<math>\varphi(9,0)</math>
|9
|12466666666
|-
|<math>\varphi(9,\varphi(9,0))</math>
|9t9
|124666666665799999999
|-
|<math>\varphi(10,0)</math>
|limit
|124666666666
|+
!序数（十进制 + Cantor 记号 + Veblen 记号）
!扩展DcN
!1-Y
|-
|<math>\varphi(10,0)</math>
|q1111111111r
|124666666666
|-
|<math>\varphi(11,0)</math>
|q11111111111r
|1246666666666
|-
|<math>\varphi(\omega,0)</math>
|qwr
|12467
|-
|<math>\varepsilon_{\varphi(\omega,0)+1}</math>
|et1qwr=qwre =q1rt1qwr=qwrq1r
|124674
|-
|<math>\varphi(\omega,1)</math>
|qwrqwr
|12467467
|-
|<math>\varphi(\omega,\omega)</math>
|qwrtw
|124675
|-
|<math>\varphi(\omega+1,0)</math>
|q1wr
|124676
|-
|<math>\varphi(\omega2,0)</math>
|qw1r
|1246767
|-
|<math>\varphi(\varepsilon_0,0)</math>
|qer
|124679
|-
|<math>\varphi(\varepsilon_0+\omega,\zeta_0)</math>
|qw1erty（qwerty）
|12467967579
|-
|<math>\varphi(\zeta_0,0)</math>
|qyr
|124679B
|-
|<math>\varphi(\varphi(\omega,0),0)</math>
|qqwrr
|124679BC
|-
|<math>\Gamma_0</math>
|limit
|12468
|}

{| class="wikitable"
!序数（十进制+BOCF）
!1-Y
|-
|<math>\psi(\Omega^{\Omega})</math>
|12468
|-
|<math>\psi(\Omega^{\Omega}+1)</math>
|124682
|-
|<math>\psi(\Omega^{\Omega}+\psi(\Omega^{\Omega}))</math>
|124682468
|-
|<math>\psi(\Omega^{\Omega}+\Omega)</math>
|124684
|-
|<math>\psi(\Omega^{\Omega}+\Omega^\omega)</math>
|12468467
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\omega)})</math>
|124684679AB
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)})</math>
|124684679AC
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)+1})</math>
|124684679AC6
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+1)})</math>
|124684679AC7
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+\Omega)})</math>
|124684679AC9
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+\Omega^\omega)})</math>
|124684679AC9AB
|-
|<math>\psi(\Omega^{\Omega}2)</math>
|12468468
|-
|<math>\psi(\Omega^{\Omega+1})</math>
|124686
|-
|<math>\psi(\Omega^{\Omega+\psi(\Omega^{\Omega})})</math>
|12468679BD
|-
|<math>\psi(\Omega^{\Omega2})</math>
|1246868
|-
|<math>\psi(\Omega^{\Omega\psi(\Omega^{\Omega})})</math>
|1246879BD
|-
|<math>\psi(\Omega^{\Omega^2})</math>
|124688
|-
|<math>\psi(\Omega^{\Omega^\omega})</math>
|124689
|-
|<math>\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})</math>
|124689BDFG
|-
|<math>\psi(\Omega^{\Omega^\Omega})</math>
|12468A
|-
|<math>\psi(\Omega_2)</math>
|1247
|-
|<math>\psi(\Omega_2+\Omega^\Omega)</math>
|1247468
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2))</math>
|124747
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\Omega))</math>
|12476
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\Omega^\Omega))</math>
|124768
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|124769
|-
|<math>\psi(\Omega_22)</math>
|12477
|-
|<math>\psi(\Omega_2\omega)</math>
|12478
|-
|<math>\psi(\Omega_2\Omega)</math>
|12479
|-
|<math>\psi(\Omega_2^2)</math>
|1247A
|-
|<math>\psi(\Omega_2^{\Omega_2})</math>
|1247AD
|-
|<math>\psi(\Omega_3)</math>
|1247B
|-
|<math>\psi(\Omega_4)</math>
|1247BG
|-
|<math>\psi(\Omega_\omega)</math>
|1248
|}
再往后涉及项嵌套的提升效应，目前对此研究不清晰，故枚举列表暂时到此为止。

{{默认排序:个人记号}}
[[分类:分析]]
[[分类:记号]]

记号展开器

2026-02-20T11:03:43Z

Baixie01000a7：

[https://hypcos.github.io/notation-explorer/ NE]包含了许多常见记号的展开器。 
以下网址也包含了一些记号的展开器，各有不同，请依据实际情况使用：

* [https://0y.googology.top 0-Y展开器(带山脉图)，i0-Y(测试性)]
* [https://solarzone1010.github.io/ SSO内的BMS分析仪，cOCF及HSPN展开器，TONF及GON浏览器等]
* [https://gyafun.jp/ln/basmat.cgi Bashicu矩阵计算器]
* [https://waffle3z.github.io/notations/ BMS、Y序列、HPrSS、LPrSS、BrSS浏览器等]
* [https://fghdisplayer.onrender.com/ LVO内韦伯伦函数的FGH及基本列展开]
* [https://naruyoko.github.io/googology/ Y和ω-Y序列的展开和山脉图绘制、BMS的展开过程演示等]
* [https://koteitan.github.io/BeklemishevsWorms/ worm序列辅助展开程序] [https://gomen520.github.io/ X-Y展开程序]

BMS

2026-02-20T10:46:41Z

Baixie01000a7：/* 数学定义 */

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。直至今日，BMS 依然是已经证明[[良序]]的最强的序数记号。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto（Racheline）剽窃了他的证明。据t est_alpha0 所说，他在 2022 年 2 月 16 日在 googology wiki 上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline 在 ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

BMS

2026-02-20T10:46:06Z

Baixie01000a7：sup -> \sup

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。直至今日，BMS 依然是已经证明[[良序]]的最强的序数记号。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto（Racheline）剽窃了他的证明。据t est_alpha0 所说，他在 2022 年 2 月 16 日在 googology wiki 上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline 在 ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

fffz分析Part5:JO~TBO

2026-02-20T10:40:52Z

Baixie01000a7：

本条目展示[[Fake Fake Fake Zeta|fffz]]分析的第五部分。使用<math>MOCF</math>和[[BMS]]对照

<nowiki>\begin{align}s\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\varepsilon_0^{\varepsilon_0}+\omega](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I+1}}(0))^2=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(1,0,0)(2,1,1)(3,1,0)(4,2,0)=\mathrm{JOJO(JO^2)}\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_1)=\psi(\psi_{\Omega_{I+1}}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_2)=\psi(\psi_{\Omega_{I+1}}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega)=\psi(\psi_{\Omega_{I+1}}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega+\varepsilon_0)=\psi(\psi_{\Omega_{I+1}}(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_{\varepsilon_0}})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)(7,1,0)(8,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\zeta_0)=\psi(\Omega_{I+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\zeta_0))=\psi(\Omega_{I+2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\zeta_0)))=\psi(\Omega_{I+3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,4,0)(7,4,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{I+\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(\Omega_{I+\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\psi_Z(\varepsilon_0^\omega\times\omega)](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\Omega_{\Omega_{\psi_{I_2}(0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega))=\psi(\psi_{I_2}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega)))=\psi(\psi_{I_2}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,3,0)(6,3,0)(7,4,1)(8,5,1)(9,4,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_2}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_2}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+3}))=\psi(\psi_{I_2}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}))=\psi(\psi_{I_2}(\Omega_{I+1}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}))=\psi(I_2\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+2}\times\omega))=\psi(I_2^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^2}\times\omega))=\psi(I_2^{I_2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^{\omega^2}}\times\omega))=\psi(I_2^{I_2^{I_2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I_2+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega)))=\psi(I_3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega))))=\psi(I_4)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,0)(11,4,1)(12,4,0)(11,0,0)\\&\large\color{red}{\psi_Z(\varepsilon_0^{\varepsilon_0})=\psi(I_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\mathrm{SIO}}\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0)=\psi(I_\omega+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0^2)=\psi(I_\omega+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times2)=\psi(I_\omega\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times3)=\psi(I_\omega\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}\times\omega](\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+1})=\psi(I_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+2})=\psi(I_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}](\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(I_{\Omega_{\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^2)=\psi(I_{\Omega_{\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^\omega)=\psi(I_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{\psi_{\Omega_{I+1}}(0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(I_{\Omega_{I+\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(I_{\Omega_{I+\omega^3}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(I_{\Omega_{I+\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0},\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega))=\psi(I_I)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_{I_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1})=\psi(\psi_{I(1,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+2})=\psi(\psi_{I(1,0)}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+3})=\psi(\psi_{I(1,0)}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\omega^\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2}\times2)=\psi(\psi_{I(1,0)}(\psi_{I(1,0)}(\psi_{I(1,0)}(\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)=\psi(I(1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega)=\psi(I(1,0)+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega,\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega)=\psi(I(1,0)+\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,0)\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,1)(6,3,1)(7,3,0)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}](\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega)=\psi(I(1,0)^{I(1,0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega)=\psi(I(1,0)^{I(1,0)^{I(1,0)}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\varepsilon_0^{\varepsilon_0\times2})=\psi(\psi_{\Omega_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\zeta_0)=\psi(\Omega_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_{I(1,0)+1}}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_{I(1,0)+1}}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0}))=\psi(I_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}))=\psi(I_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega)=\psi(\psi_{I(1,1)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1}))=\psi(\psi_{I(1,1)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))))=\psi(I(1,3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,1)(11,4,1)(12,4,0)(11,4,1)(12,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+1})=\psi(I(1,\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+2})=\psi(I(1,\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega})=\psi(I(1,\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,I_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times2)=\psi(I(1,I(1,\Omega)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times3)=\psi(I(1,I(1,I(1,\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega)=\psi(\psi_{I(2,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega+1})=\psi(\psi_{I(2,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega\times2})=\psi(\psi_{I(2,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega)=\psi(I(2,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times3})=\psi(I(2,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega)=\psi(\psi_{I(3,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega)=\psi(I(3,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega)=\psi(I(4,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\large\color{blue}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}](\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)=\mathrm{MBO}}\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0)=\psi(I(\Omega_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{2})=\psi(I(\Omega_{\omega^2},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\omega^\omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\Omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega)=\psi(I(\psi_I(0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega+1})=\psi(I(\psi_I(\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I(I_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0+\omega})=\psi(I(I_\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(1,\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times2+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(1,\omega),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times3+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(I(1,\omega),0),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\LARGE\color{purple}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)=\psi(\psi_{I(1,0,0)}(0))=\psi((2~~1-)^{1,0})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)=\mathrm{TBO}}\end{align}</nowiki>

__静态重定向__
[[分类:分析]]

fffz分析Part4:JO~TBO

2026-02-20T10:40:39Z

Baixie01000a7：Baixie01000a7移动页面fffz分析Part4:JO~TBO至fffz分析Part5:JO~TBO：标题有错别字

#重定向 [[fffz分析Part5:JO~TBO]]

fffz分析Part5:JO~TBO

2026-02-20T10:40:39Z

Baixie01000a7：Baixie01000a7移动页面fffz分析Part4:JO~TBO至fffz分析Part5:JO~TBO：标题有错别字

本条目展示[[Fake Fake Fake Zeta|fffz]]分析的第五部分（标题打错了）。使用<math>MOCF</math>和[[BMS]]对照

<nowiki>\begin{align}s\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\varepsilon_0^{\varepsilon_0}+\omega](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I+1}}(0))^2=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(1,0,0)(2,1,1)(3,1,0)(4,2,0)=\mathrm{JOJO(JO^2)}\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_1)=\psi(\psi_{\Omega_{I+1}}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_2)=\psi(\psi_{\Omega_{I+1}}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega)=\psi(\psi_{\Omega_{I+1}}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega+\varepsilon_0)=\psi(\psi_{\Omega_{I+1}}(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_{\varepsilon_0}})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)(7,1,0)(8,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\zeta_0)=\psi(\Omega_{I+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\zeta_0))=\psi(\Omega_{I+2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\zeta_0)))=\psi(\Omega_{I+3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,4,0)(7,4,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{I+\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(\Omega_{I+\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\psi_Z(\varepsilon_0^\omega\times\omega)](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\Omega_{\Omega_{\psi_{I_2}(0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega))=\psi(\psi_{I_2}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega)))=\psi(\psi_{I_2}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,3,0)(6,3,0)(7,4,1)(8,5,1)(9,4,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_2}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_2}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+3}))=\psi(\psi_{I_2}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}))=\psi(\psi_{I_2}(\Omega_{I+1}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}))=\psi(I_2\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+2}\times\omega))=\psi(I_2^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^2}\times\omega))=\psi(I_2^{I_2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^{\omega^2}}\times\omega))=\psi(I_2^{I_2^{I_2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I_2+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega)))=\psi(I_3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega))))=\psi(I_4)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,0)(11,4,1)(12,4,0)(11,0,0)\\&\large\color{red}{\psi_Z(\varepsilon_0^{\varepsilon_0})=\psi(I_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\mathrm{SIO}}\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0)=\psi(I_\omega+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0^2)=\psi(I_\omega+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times2)=\psi(I_\omega\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times3)=\psi(I_\omega\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}\times\omega](\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+1})=\psi(I_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+2})=\psi(I_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}](\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(I_{\Omega_{\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^2)=\psi(I_{\Omega_{\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^\omega)=\psi(I_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{\psi_{\Omega_{I+1}}(0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(I_{\Omega_{I+\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(I_{\Omega_{I+\omega^3}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(I_{\Omega_{I+\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0},\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega))=\psi(I_I)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_{I_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1})=\psi(\psi_{I(1,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+2})=\psi(\psi_{I(1,0)}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+3})=\psi(\psi_{I(1,0)}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\omega^\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2}\times2)=\psi(\psi_{I(1,0)}(\psi_{I(1,0)}(\psi_{I(1,0)}(\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)=\psi(I(1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega)=\psi(I(1,0)+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega,\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega)=\psi(I(1,0)+\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,0)\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,1)(6,3,1)(7,3,0)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}](\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega)=\psi(I(1,0)^{I(1,0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega)=\psi(I(1,0)^{I(1,0)^{I(1,0)}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\varepsilon_0^{\varepsilon_0\times2})=\psi(\psi_{\Omega_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\zeta_0)=\psi(\Omega_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_{I(1,0)+1}}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_{I(1,0)+1}}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0}))=\psi(I_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}))=\psi(I_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega)=\psi(\psi_{I(1,1)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1}))=\psi(\psi_{I(1,1)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))))=\psi(I(1,3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,1)(11,4,1)(12,4,0)(11,4,1)(12,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+1})=\psi(I(1,\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+2})=\psi(I(1,\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega})=\psi(I(1,\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,I_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times2)=\psi(I(1,I(1,\Omega)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times3)=\psi(I(1,I(1,I(1,\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega)=\psi(\psi_{I(2,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega+1})=\psi(\psi_{I(2,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega\times2})=\psi(\psi_{I(2,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega)=\psi(I(2,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times3})=\psi(I(2,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega)=\psi(\psi_{I(3,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega)=\psi(I(3,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega)=\psi(I(4,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\large\color{blue}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}](\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)=\mathrm{MBO}}\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0)=\psi(I(\Omega_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{2})=\psi(I(\Omega_{\omega^2},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\omega^\omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\Omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega)=\psi(I(\psi_I(0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega+1})=\psi(I(\psi_I(\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I(I_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0+\omega})=\psi(I(I_\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(1,\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times2+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(1,\omega),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times3+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(I(1,\omega),0),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\LARGE\color{purple}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)=\psi(\psi_{I(1,0,0)}(0))=\psi((2~~1-)^{1,0})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)=\mathrm{TBO}}\end{align}</nowiki>

__静态重定向__
[[分类:分析]]

MMS

2026-02-20T10:26:12Z

Baixie01000a7：

变异矩阵系统（Mutant Martix System，MMS）最初是 Aarex 于 2023 年提出的记号，它是 [[BMS]] 的一个强大的推广。后来其规则经过多次的调整和完善，其中被广泛使用的是 HypCos 的 MM3（Mutant Martix 3）。不过MM3已于2026年2月6日被发现[[无穷降链]]，现在已转变为使用Weak MMS。

我们下面对其规则进行简要的介绍。

== 定义 ==
MM3 是以矩阵形式表达的表达式，每个元素具有表观行标和内在行标。以下陈述中，“左”的列标比“右”小，“上”的行标比“下”小。

* 表观行标：一个元素的表观行标就是它写在表达式中的一列的第几个元素，它是正整数。
* 内在行标：内在行标是序数。表观行标为 1 的元素，内在行标也为 1。对于表观行标大于 1 的元素 x，找到它上方最近的不等于 x 的元素 y，x 与 y 的表观行标差为 n，那么 x 的内在行标是 (y 的内在行标)+ωn−1。
* 待定父元：内在行标为 1 的元素，它的待定父元是它向左一格。对于内在行标大于 1 的元素 x，先向左走到 x 上方元素的父元所在列，找到该列之中满足“内在行标小于等于 x 之内在行标，而且值大于等于 x − 1”的最下元素，它就是 x 的待定父元。
* 父元：从一个元素 x 出发，不断取待定父元的待定父元……的待定父元，直到初次遇到等于 x − 1 的元素为止，它就是 x 的父元。
* 祖先：祖先元素是父关系的自反[[传递闭包#关系的传递闭包|传递闭包]]。也就是包括自身、父元、父元的父元、父元的父元的父元、……。
* 待定根元素：从 LNZ 出发。向左或向左上走到最近的等于 LNZ−1 的祖先元素，该元素成为待定根元素。向上一格（表观行标减 1）。重复以上两步，直到表观行标到达 0，无法再取任何元素为止。
* 根元素：计数每一列的待定根元素，去掉零值，并记作这些数值是从哪一列来的。最左边添加一个“1”，得到提取序列。提取序列按照 [[初等序列系统|PrSS]] 规则找根元素，这个根元素向右一格，回到原矩阵中对应的列，该列最上的待定根元素，就是真正的根元素。
* 减一操作：展开一轮的第一步是将最右列“减一”。具体操作是，把待定根元素及其下方的所有元素复制到最右列，列标与内在行标平移，使得待定根元素恰好复制到（取代掉）LNZ 的位置。
* 根列元素：待定根元素及其上方同列的所有元素，每个都是“根列元素”。注意，不包括待定根元素下方的元素。
* magma 元素：每个根列元素都对应一些 magma 元素。从该根列元素出发，所有内在行标与之相等的后代元素（与祖先相对），就是该根列元素对应的 magma 元素。
* 参考元素：最右列的元素 x 是参考元素。x 要对应到内在行标小于（x 下方一格的元素的内在行标）的最下根列元素。
* 延伸：这是展开一轮的第二步。将减一之前的表达式中，根列右方（不含根列，包括减一前的最右列）的元素一列一列地复制出来。每一列从上到下复制。一个源元素复制时可能有值的提升、行标的提升。所有提升由本列最近一次经过的 magma 元素，以及它对应的根列元素对应的最下参考元素，二者决定。magma 元素复制时可能产生多个复制品。它对应的根列元素对应的参考元素可能有多个，每个产生一个复制品。

== 分析 ==
''主词条：[[MM3 vs ω-Y]]''{{默认排序:序数记号}}
[[分类:记号]]

无穷降链

2026-02-20T10:08:54Z

Baixie01000a7：

在googology中，无穷降链是一个重要概念。一个记号没有无穷降链是其良定义的必要条件。

== 定义 ==
无穷降链指的是一个无穷序列a_1,a_2,a_3......满足：

a_1>a_2>a_3>......，即该序列集合中不存在最小的项。

一个记号[[良序]]等价于其没有无穷降链。

== 例子 ==
例如，[[元素属性|坏根]]始终为第一项的[[PrSS]]：

1,2,2展开为1,2,1,2,1,2......

1,2,1,2展开为1,2,1,1,2,1,1,2,1,1,2...

1,2,1,1,2展开为1,2,1,1,1,2,1,1,1,2,1,1,1,2...

因此，我们需要知道1,2,2有多大，就需要知道1,2,1,2有多大，而要知道1,2,1,2有多大，又需要知道1,2,1,1,2有多大....以此类推，这个集合里不存在一个最小的序列能让我们知道其大小，因而我们无法知道1,2,2的实际大小。
[[分类:重要概念]]

IBLP分析Part2

2026-02-20T07:49:00Z

Baixie01000a7：创建页面，内容为“{| class="wikitable" |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3 |1,2,4,8,10 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2 |1,2,4,8,10,6 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1 |1,2,4,8,10,6,9 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3 |1,2,4,8,10,6,10 |-…”

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|-
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|1,2,4,8,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,2,4,8,13,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2
|1,2,4,8,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3
|1,2,4,8,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,8,6,4)3
|1,2,4,8,13,18,23,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1
|1,2,4,8,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1(12,11,10,9)2(13,12,11,10,9)3
|1,2,4,8,13,19,25,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,10,9)1(12,11,10,9)2(13,12,11,10,9)3(14,13,12)1
|1,2,4,8,13,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3
|1,2,4,8,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,9,8,6,4)3(13,*12,9,8,6,4)3
|1,2,4,8,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4
|1,2,4,8,13,20,27,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4(14,12,10)1
|1,2,4,8,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4
|1,2,4,8,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1
|1,2,4,8,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1(10,9,6,4)2(11,10,9,6,4)3(12,*11,10,9,6,4)3(13,11,9,6,4)3(14,*13,11,10,9,6,4)4(15,*13,11,10,9,6,4)4
|1,2,4,8,14,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,*6,4,3,2,1,0)4
|1,2,4,8,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7)1
|1,2,4,8,14,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,2,4,8,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4
|1,2,4,8,14,18,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9)1
|1,2,4,8,14,18,24,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,2,4,8,14,18,24,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2
|1,2,4,8,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,*6,4,3,2,1,0)4
|1,2,4,8,14,19,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,2,1,0)3(10,*9,7,3,2,1,0)4
|1,2,4,8,14,19,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,6,4)2
|1,2,4,8,14,19,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3
|1,2,4,8,14,19,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10)1
|1,2,4,8,14,19,23,29,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,19,23,29,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3
|1,2,4,8,14,19,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,7,6,4)3
|1,2,4,8,14,19,24,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1
|1,2,4,8,14,19,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,2,4,8,14,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*14,12,11,10,9,8)4
|1,2,4,8,14,19,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*6,4,3,2,1,0)4
|1,2,4,8,14,20,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2
|1,2,4,8,14,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3
|1,2,4,8,14,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4(13,8,7,6,4)(14,*13,8,3,2,1,0)4
|1,2,4,8,14,20,26,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,7,6,4)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,2,4,8,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4(12,*9,8,3,2,1,0)4
|1,2,4,8,14,22,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,7,6,4)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,12,11)1
|1,2,4,8,14,22,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,22,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,10,9,8)2(15,14,10,9,8)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,30,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,10,9,8)3(15,*14,13,3,2,1,0)4
|1,2,4,8,14,22,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,14,22,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3
|1,2,4,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3(14,12,2,1,0)3(15,*14,12,11,2,1,0)4(16,15,14,12)2(17,16,15,14,12)3(18,*17,16,15,14,12)3
|1,2,4,8,15,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,3,2,1,0)3(12,*11,3,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3
|1,2,4,8,15,12,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,6,4)1
|1,2,4,8,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4
|1,2,4,8,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4(12,11,6,4)2(13,12,11,6,4)3(14,*13,12,11,6,4)3
|1,2,4,8,15,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4
|1,2,4,8,15,14,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4(13,12,11,7)2(14,13,12,11,7)3(15,*14,13,12,11,7)3
|1,2,4,8,15,14,23,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2
|1,2,4,8,15,14,23,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,7,6,4)3(15,*14,12,3,2,1,0)4
|1,2,4,8,15,14,23,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,11)1
|1,2,4,8,15,14,23,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,7,6,4)3(15,*14,13,3,2,1,0)4
|1,2,4,8,15,14,23,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,15,14,23,20,28,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,2,4,8,15,14,23,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,12,11)1
|1,2,4,8,15,14,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4(18,17,12,11)2(19,18,17,12,11)3(20,*19,18,17,12,11)3
|1,2,4,8,15,14,23,22,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,13,12,11)2
|1,2,4,8,15,14,23,22,33,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,7,6,4)3
|1,2,4,8,15,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3
|1,2,4,8,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,17,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,2,1,0)3
|1,2,4,8,15,17,14,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,12,11,8)2(14,13,12,11,8)3(15,*14,13,12,11,8)3
|1,2,4,8,15,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3
|1,2,4,8,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,20,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3
|1,2,4,8,15,20,14,23,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3(19,14,13,12)2(20,19,14,13,12)3(21,*20,19,14,13,12)3
|1,2,4,8,15,20,14,23,28,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,14,13,12)3
|1,2,4,8,15,20,14,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,20,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,8,7,6,4)3
|1,2,4,8,15,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,11,7,6,4)3
|1,2,4,8,15,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,11,8)1
|1,2,4,8,15,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,3,2,1,0)4
|1,2,4,8,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,7,6,4)3
|1,2,4,8,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,7,6,4)3(13,8,7,6,4)3(14,*13,8,7,6,4)3
|1,2,4,8,15,22,22
|-
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|1,2,4,8,15,22,27
|-
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|1,2,4,8,15,22,28
|-
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|1,2,4,8,15,22,29
|-
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|1,2,4,8,15,22,29,29
|-
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|1,2,4,8,15,22,29,36
|-
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|1,2,4,8,15,23
|-
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|-
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|1,2,4,8,15,25
|-
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|1,2,4,8,15,25,25
|-
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|1,2,4,8,15,25,27
|-
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|1,2,4,8,15,25,30
|-
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|1,2,4,8,15,25,32
|-
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|1,2,4,8,15,25,32,39
|-
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|1,2,4,8,15,25,33
|-
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|1,2,4,8,15,25,35
|-
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|1,2,4,8,15,25,36
|-
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|1,2,4,8,15,25,39
|-
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|1,2,4,8,15,25,39,50
|-
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|1,2,4,8,15,26
|-
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|1,2,4,8,15,26,26
|-
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|1,2,4,8,15,26,28
|-
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|1,2,4,8,15,26,30
|-
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|1,2,4,8,15,26,31
|-
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|1,2,4,8,15,26,33
|-
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|1,2,4,8,15,26,34
|-
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|1,2,4,8,15,26,37
|-
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|1,2,4,8,15,26,40
|-
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|1,2,4,8,15,26,41
|-
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|1,2,4,8,16
|}
{| class="wikitable"
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|1,2,4,8,16,8,16
|-
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|1,2,4,8,16,10
|-
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|1,2,4,8,16,11,8
|-
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|-
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|-
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|1,2,4,8,16,12
|-
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|-
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|-
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|1,2,4,8,16,12,20,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,11,2,1,0)3(20,*19,11,3,2,1,0)4
|1,2,4,8,16,12,20,16,24,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,11,9)1
|1,2,4,8,16,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4
|1,2,4,8,16,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2
|1,2,4,8,16,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,3,2,1,0)4
|1,2,4,8,16,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3
|1,2,4,8,16,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3(23,21,19,11,9)3(24,*23,21,20,19,11,9)4(25,*24,*23,21,20,19,11,9)4
|1,2,4,8,16,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2
|1,2,4,8,16,14,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,3,2,1,0)4
|1,2,4,8,16,14,22,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3
|1,2,4,8,16,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3(22,20,12,11,9)3(23,*22,20,19,12,11,9)4(,24,*23,*22,20,19,12,11,9)4
|1,2,4,8,16,15,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3
|1,2,4,8,16,15,27,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3
|1,2,4,8,16,15,27,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3(21,19,12,11,9)3(22,*21,19,13,12,11,9)
4(23,22,21,19)2(24,23,22,21,19)3(25,*24,23,22,21,19)3(26,24,22,21,19)3(27,*26,24,23,22,21,19)4(28,*27,*26,24,23,22,21,19)4
|1,2,4,8,16,15,27,22,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,*12,*11,9,3,2,1,0)4
|1,2,4,8,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3
|1,2,4,8,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3
|1,2,4,8,16,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3(13,11,2,1,0)3(14,*13,11,10,2,1,0)4(15,*14,*13,11,10,2,1,0)4
|1,2,4,8,16,19,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,2,4,8,16,19,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4
|1,2,4,8,16,19,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,12,10)1
|1,2,4,8,16,19,12,20,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,*12,10,3,2,1,0)4
|1,2,4,8,16,19,12,20,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3
|1,2,4,8,16,19,12,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3(23,21,13,12,10)3(24,*23,21,20,13,12,10)4(25,*24,*23,21,20,13,12,10)4
|1,2,4,8,16,19,12,20,19,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,14,13,12,10)3(21,*20,14,13,12,10)3(22,20,13,12,10)3(23,*22,20,14,13,12,10)4(24,*23,*22,20,14,13,12,10)4
|1,2,4,8,16,19,12,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3
|1,2,4,8,16,19,12,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,2,1,0)2(22,21,2,1,0)3(23,*22,21,2,1,0)3
|1,2,4,8,16,19,12,20,23,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,14,13,12,10)3(22,*21,14,13,12,11,10)3(23,21,13,12,10)3(24,*23,21,14,13,12,10)4(25,*24,*23,21,14,13,12,10)4
|1,2,4,8,16,19,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4
|1,2,4,8,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,20,15)1
|1,2,4,8,16,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,21,20,15)
2(23,22,21,20,15)3(24,*23,22,21,20,15)3(25,23,21,20,15)3(26,*25,23,22,21,20,15)4(27,*26,*25,23,22,21,20,15)4
|1,2,4,8,16,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,13,12,10)3
|1,2,4,8,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,2,4,8,16,21,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,4,2,1,0)4
|1,2,4,8,16,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,2,1,0)4
|1,2,4,8,16,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,4)1
|1,2,4,8,16,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4
|1,2,4,8,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4
|1,2,4,8,16,22,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,2,1,0)3(22,*21,16,3,2,1,0)
4(23,22,21,16)2(24,23,22,21,16)3(25,*24,23,22,21,16)3(26,24,22,21,16)3(27,*26,24,23,22,21,16)4(28,*27,*26,24,23,22,21,16)4
|1,2,4,8,16,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,14,13,11)3(22,*21,16,15,14,13,11)4(23,15,14,13,11)3(24,*23,15,14,13,11)3(25,23,14,13,11)3(26,*25,23,15,14,13,11)4
|1,2,4,8,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,2,4,8,16,23,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,4,2,1,0)3
|1,2,4,8,16,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3
|1,2,4,8,16,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,16,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,4)1
|1,2,4,8,16,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*9,4,3,2,1,0)4
|1,2,4,8,16,23,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2
|1,2,4,8,16,23,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3
|1,2,4,8,16,23,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3(14,12,10,9,4)3(15,*14,12,11,10,9,4)4(16,*15,*14,12,11,10,9,4)4
|1,2,4,8,16,23,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*10,*9,4,3,2,1,0)4
|1,2,4,8,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,*13,*12,9,4,3,2,1,0)5
|1,2,4,8,16,24,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,6)1
|1,2,4,8,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4
|1,2,4,8,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,3,2,1,0)3(14,*13,3,2,1,0)3(15,13,2,1,0)3(16,*15,13,3,2,1,0)4(17,*16,*15,13,3,2,1,0)4
|1,2,4,8,16,27,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5(14,*9,6,3,2,1,0)4(15,*14,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2
|1,2,4,8,16,28,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4
|1,2,4,8,16,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,13,12)1
|1,2,4,8,16,28,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,*13,12,3,2,1,0)4(17,*16,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,14,13,12)2
|1,2,4,8,16,28,44,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,10,9,6)3
|1,2,4,8,16,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*10,*0,6,4,3,2,1,0)5
|1,2,4,8,16,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,2,1,0)3(13,*12,11,3,2,1,0)4(14,*13,*12,11,4,3,2,1,0)5
|1,2,4,8,16,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3
|1,2,4,8,16,30,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5
|1,2,4,8,16,30,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,14,12)1
|1,2,4,8,16,30,45
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,16,15,14,12)3
|1,2,4,8,16,30,52,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
|1,2,4,8,16,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
(17,14,10,9,6)3(18,*17,14,11,10,9,6)4(19,*18,*17,14,12,11,10,9,6)5(20,19,18,17,14)3(21,*20,19,18,17,14)3(22,20,18,17,16)3(23,*22,20,19,18,17,14)4(24,*23,*22,20,19,18,17,14)4
|1,2,4,8,16,31,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5(13,9,2,1,0)3(14,*13,9,3,2,1,0)4(15,*14,*13,9,4,3,2,1,0)5(16,*15,*14,*13,9,6,4,3,2,1,0)6(17,*16,*15,*14,*13,9,6,4,3,2,1,0)6
|1,2,4,8,16,32,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|}

MMS

2026-02-20T07:23:41Z

Baixie01000a7：

变异矩阵系统（Mutant Martix System，MMS）最初是 Aarex 于 2023 年提出的记号，它是 [[BMS]] 的一个强大的推广。后来其规则经过多次的调整和完善，目前使用的是 HypCos 的 MM3（Mutant Martix 3）。MM3已于2026年2月6日被发现无穷降链。

我们下面对其规则进行简要的介绍。

== 定义 ==
MM3 是以矩阵形式表达的表达式，每个元素具有表观行标和内在行标。以下陈述中，“左”的列标比“右”小，“上”的行标比“下”小。

* 表观行标：一个元素的表观行标就是它写在表达式中的一列的第几个元素，它是正整数。
* 内在行标：内在行标是序数。表观行标为 1 的元素，内在行标也为 1。对于表观行标大于 1 的元素 x，找到它上方最近的不等于 x 的元素 y，x 与 y 的表观行标差为 n，那么 x 的内在行标是 (y 的内在行标)+ωn−1。
* 待定父元：内在行标为 1 的元素，它的待定父元是它向左一格。对于内在行标大于 1 的元素 x，先向左走到 x 上方元素的父元所在列，找到该列之中满足“内在行标小于等于 x 之内在行标，而且值大于等于 x − 1”的最下元素，它就是 x 的待定父元。
* 父元：从一个元素 x 出发，不断取待定父元的待定父元……的待定父元，直到初次遇到等于 x − 1 的元素为止，它就是 x 的父元。
* 祖先：祖先元素是父关系的自反[[传递闭包#关系的传递闭包|传递闭包]]。也就是包括自身、父元、父元的父元、父元的父元的父元、……。
* 待定根元素：从 LNZ 出发。向左或向左上走到最近的等于 LNZ−1 的祖先元素，该元素成为待定根元素。向上一格（表观行标减 1）。重复以上两步，直到表观行标到达 0，无法再取任何元素为止。
* 根元素：计数每一列的待定根元素，去掉零值，并记作这些数值是从哪一列来的。最左边添加一个“1”，得到提取序列。提取序列按照 [[初等序列系统|PrSS]] 规则找根元素，这个根元素向右一格，回到原矩阵中对应的列，该列最上的待定根元素，就是真正的根元素。
* 减一操作：展开一轮的第一步是将最右列“减一”。具体操作是，把待定根元素及其下方的所有元素复制到最右列，列标与内在行标平移，使得待定根元素恰好复制到（取代掉）LNZ 的位置。
* 根列元素：待定根元素及其上方同列的所有元素，每个都是“根列元素”。注意，不包括待定根元素下方的元素。
* magma 元素：每个根列元素都对应一些 magma 元素。从该根列元素出发，所有内在行标与之相等的后代元素（与祖先相对），就是该根列元素对应的 magma 元素。
* 参考元素：最右列的元素 x 是参考元素。x 要对应到内在行标小于（x 下方一格的元素的内在行标）的最下根列元素。
* 延伸：这是展开一轮的第二步。将减一之前的表达式中，根列右方（不含根列，包括减一前的最右列）的元素一列一列地复制出来。每一列从上到下复制。一个源元素复制时可能有值的提升、行标的提升。所有提升由本列最近一次经过的 magma 元素，以及它对应的根列元素对应的最下参考元素，二者决定。magma 元素复制时可能产生多个复制品。它对应的根列元素对应的参考元素可能有多个，每个产生一个复制品。

== 分析 ==
''主词条：[[MM3 vs ω-Y]]''{{默认排序:序数记号}}
[[分类:记号]]

BHM

2026-02-20T07:19:35Z

Baixie01000a7：

Bashicu超矩阵(Bashicu Hyper Matrix,'''BHM''')是Bashicu Hyudora发明的序数记号。它是[[BMS]]的一个运用[[急模式]]的改版。目前BHM还未被证明良序。

== 定义 ==
''提示：阅读BHM定义之前首先需要阅读[[BMS#正式定义|BMS的定义]]。''

BHM和BMS的规则除了坏根的寻找之外没有区别，如父项、祖先项、好部、坏部、阶差向量、不提升规则，因此这里不再赘述。以下介绍BHM坏根寻找的规则：

# 第0列：默认行、列标均从1开始，并在第1列之前加上一个额外的没有值的第0列。如果BHM中一个元素没有父项，则取其父项为同行第0列的元素。
# '''子项'''：如果项A的父项是项B，则称A是B的子项。
# '''待定坏根'''：待定坏根为末列最靠下的非0项的父项的父项的子项所在列。特别的，如果末列最下非0项不在第1行，则要求待定坏根正上方的元素应当是末列最下非0项正上方的元素的祖先项。
# '''预展开'''：根据找到的待定坏根，确定待定好部G'，待定坏部B'，末列L，待定阶差向量<math>\Delta'</math>，随后'''按照BMS的规则'''得到<math>G'\sim B'\sim (B'+\Delta') \sim (L+\Delta')</math>.(其中~是序列连接)。特别的，我们称最右侧的待定坏根（即BMS意义的坏根）对应的预展开式为'''基准式'''。
# '''小根'''：在字典序下，预展开式小于基准式的待定坏根称为小根。特别的，如果小根不存在，则规定第0列为小根。真正的坏根是在所有小根右侧的第一个待定坏根。确定坏根后，只需要按BMS规则找好部、坏部、阶差向量即可展开。

举例：

# 考虑BHM表达式<math>(0)(1)(2)(1)(1)(2)</math>,首先找到末列最下非0项父项的父项的所有子项（红色标出）：<math>(0)({\color{red}1})(2)({\color{red}1})({\color{red}1})(2)</math>.于是我们得知待定坏根是第二列、第四列、第五列。首先得到第五列的预展开式（基准列）：<math>(0)(1)(2)(1)(1)(1)(2)</math>.随后得到第四列的预展开式<math>(0)(1)(2)(1)(1)(1)(1)(2)</math>.随后得到第二列的预展开式<math>(0)(1)(2)(1)(1)(1)(2)(1)(1)(2)</math>.发现小根是第四列。因此真坏根是第五列。于是得到展开式：<math>(0)(1)(2)(1)(1)(1)(1)\cdots</math>
# 考虑BHM表达式<math>(0,0)(1,1)(1,0)(2,0)</math>.首先找到末列最下非0项（第四列第一行的2）的父项的父项（红色标出）：<math>({\color{red}0},0)(1,1)(1,0)(2,0)</math>.随后我们找到它所有子项（绿色标出）：<math>({\color{red}0},0)({\color{green}1},1)({\color{green}1},0)(2,0)</math>。因此我们得知第二列和第三列是待定坏根。于是我们进行预展开，得到第三列的预展开式（也是基准式）为：<math>(0,0)(1,1)(1,0)(1,0)(2,0)</math>.得到第二列的预展开式是<math>(0,0)(1,1)(1,0)(1,1)(1,0)(2,0)</math>，它在字典序上大于基准式。因此我们发现不存在小根，因此小根是第0列。坏根是第二列。于是我们得到展开式：<math>(0,0)(1,1)(1,0)(1,1)(1,0)(1,1)(1,0)\cdots</math>
# 考虑BHM表达式<math>(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)</math>,首先我们寻找待定坏根。注意到末列最下非0项不在第1行，因此待定坏根还要满足它正上方的元素应当是末列最下非0项正上方的元素的祖先项。于是我们找到待定坏根（红色标出）：<math>(0,{\color{red}0})(1,1)(1,0)(2,0)(1,1)(1,0)(1,{\color{red}0})(2,1)(2,0)(3,0)(2,1)</math>.因此我们得知第一列和第七列是待定坏根。于是我们进行预展开，得到第七列的预展开式，即基准式为<math>(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)</math>.再得到第一列的预展开式是<math>(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(3,1)</math>.发现不存在小根，于是小根是第0列，坏根是第1列。得到展开式为<math>(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)\cdots</math>

== 枚举和强度分析 ==
主词条：[[BHM分析]]

对BHM进行强度分析的难度远高于BMS。目前我们还不知道它的极限和BMS的极限的关系。目前最新的结论是<math>BHM(0,0,0)(1,1,1)=BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_\omega)</math>。梅天狸认为BHM=BMS的可能性很大。

{{默认排序:序数记号}}
[[分类:记号]]

BHM分析Part1：0~FSO

2026-02-20T07:18:01Z

Baixie01000a7：撤销Baixie01000a7（讨论）的修订版本2675

本条目展示[[BHM]]强度分析的第一部分。使用<math>veblen</math>函数。

<nowiki>\begin{aligned} & \varnothing=0\\&(0)=1\\&(0)(0)=2\\&(0)(1)=\omega\\&(0)(1)(0)=\omega+1\\&(0)(1)(0)(0)=\omega+2\\&(0)(1)(0)(0)(1)=\omega\times2\\&(0)(1)(0)(0)(1)(0)=\omega\times2+1\\&(0)(1)(0)(0)(1)(0)(0)(1)=\omega\times3\\&(0)(1)(0)(1)=\omega^2\\&(0)(1)(0)(1)(0)=\omega^2+1\\&(0)(1)(0)(1)(0)(0)(1)=\omega^2+\omega\\&(0)(1)(0)(1)(0)(0)(1)(0)(0)(1)=\omega^2+\omega\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times3\\&(0)(1)(0)(1)(0)(1)=\omega^3\\&(0)(1)(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(1)=\omega^3\times2\\&(0)(1)(0)(1)(0)(1)(0)(1)=\omega^4\\&(0)(1)(1)=\omega^\omega\\&(0)(1)(1)(0)(0)(1)=\omega^\omega+\omega\\&(0)(1)(1)(0)(0)(1)(0)(1)=\omega^\omega+\omega^2\\&(0)(1)(1)(0)(0)(1)(1)=\omega^\omega\times2\\&(0)(1)(1)(0)(1)=\omega^{\omega+1}\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)=\omega^{\omega+1}+\omega^\omega\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)(0)(1)=\omega^{\omega+1}\times2\\&(0)(1)(1)(0)(1)(0)(1)=\omega^{\omega+2}\\&(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times2}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)=\omega^{\omega\times2+1}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times3}\\&(0)(1)(1)(0)(1)(1)=\omega^{\omega^2}\\&(0)(1)(1)(0)(1)(1)(0)(1)=\omega^{\omega^2+1}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega^2+\omega}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^2\times2}\\&(0)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^3}\\&(0)(1)(1)(1)=\omega^{\omega^\omega}\\&(0)(1)(1)(1)(0)(0)(1)(1)(1)=\omega^{\omega^\omega}\times2\\&(0)(1)(1)(1)(0)(1)=\omega^{\omega^\omega+1}\\&(0)(1)(1)(1)(0)(1)(0)(1)(1)(1)=\omega^{\omega^\omega\times2}\\&(0)(1)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+1}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+2}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega\times2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^3}}\\&(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^\omega}}\\&(0)(1)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^\omega}}}\\&(0)(1)(2)=\varepsilon_0\\&(0)(1)(2)(0)(0)(1)(2)=\varepsilon_0\times2\\&(0)(1)(2)(0)(1)=\omega^{\varepsilon_0+1}\\&(0)(1)(2)(0)(1)(0)(1)=\omega^{\varepsilon_0+2}\\&(0)(1)(2)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega\times2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega^2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)=\omega^{\varepsilon_0+\omega^\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)(1)=\omega^{\varepsilon_0+\omega^{\omega^\omega}}\\&(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times2}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)=\omega^{\varepsilon_0\times2+1}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times3}\\&(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(0)(1)(1)(0)(1)=\omega^{\omega^{\varepsilon_0+1}+1}\\&(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}\times2}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+2}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega^\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(2)=\omega^{\omega^{\varepsilon_0\times2}}\\&(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}\\&(0)(1)(2)(0)(1)(2)=\varepsilon_1\\&(0)(1)(2)(0)(1)(2)(0)(1)=\omega^{\varepsilon_1+1}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_1+\varepsilon_0}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_1\times2}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_1+1}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_1+1}}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(2)=\varepsilon_2\\&(0)(1)(2)(1)=\varepsilon_\omega\\&(0)(1)(2)(1)(0)(1)=\omega^{\varepsilon_\omega+1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_\omega+\varepsilon_1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(1)=\omega^{\varepsilon_\omega\times2}\\&(0)(1)(2)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_\omega+1}}\\&(0)(1)(2)(1)(0)(1)(2)=\varepsilon_{\omega+1}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)=\varepsilon_{\omega+2}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega\times2}\\&(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^2}\\&(0)(1)(2)(1)(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^3}\\&(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega}\\&(0)(1)(2)(1)(1)(0)(1)(2)=\varepsilon_{\omega^\omega+1}\\&(0)(1)(2)(1)(1)(0)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega\times2}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)=\varepsilon_{\omega^{\omega+1}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega\times2}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^2}}\\&(0)(1)(2)(1)(1)(1)=\varepsilon_{\omega^{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)=\varepsilon_{\varepsilon_0+1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_2}\\&(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_\omega}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\omega+1}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega\times2}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^2}}\\&(0)(1)(2)(1)(1)(2)(1)(1)=\varepsilon_{\varepsilon_{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(1)=\varepsilon_{\varepsilon_{\omega^{\omega^\omega}}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_1}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\varepsilon_\omega}}\\&(0)(1)(2)(1)(2)=\zeta_0\\&(0)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(0)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\zeta_0\times2}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0\times2}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_1\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_2\\&(0)(1)(2)(1)(2)(1)=\zeta_\omega\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)=\zeta_{\omega+1}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega\times2}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^2}\\&(0)(1)(2)(1)(2)(1)(1)=\zeta_{\omega^\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\varepsilon_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)=\zeta_{\varepsilon_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_{\varepsilon_0}}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_1}</nowiki><nowiki>\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)=\zeta_{\zeta_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\zeta_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_{\zeta_0}}\\&(0)(1)(2)(1)(2)(1)(2)=\eta_0\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(2)=\eta_1\\&(0)(1)(2)(1)(2)(1)(2)(1)=\eta_\omega\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)=\eta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\eta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(2)=\eta_{\eta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(4,0)\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(5,0)\\&(0)(1)(2)(2)=\varphi(\omega,0)\\&(0)(1)(2)(2)(0)(1)(2)=\varphi(1,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)=\varphi(2,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)(1)(2)=\varphi(3,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,1)\\&(0)(1)(2)(2)(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,2)\\&(0)(1)(2)(2)(1)=\varphi(\omega,\omega)\\&(0)(1)(2)(2)(1)(1)(2)=\varphi(\omega,\varphi(1,0))\\&(0)(1)(2)(2)(1)(1)(2)(1)(2)=\varphi(\omega,\varphi(2,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,\varphi(\omega,0)))\\&(0)(1)(2)(2)(1)(2)=\varphi(\omega+1,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)=\varphi(\omega+2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times3,0)\\&(0)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)=\varphi(\omega^2+1,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2\times2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^3,0)\\&(0)(1)(2)(2)(2)=\varphi(\omega^\omega,0)\\&(0)(1)(2)(2)(2)(1)(2)=\varphi(\omega^\omega+1,0)\\&(0)(1)(2)(2)(2)(1)(2)(2)=\varphi(\omega^{\omega+1},0)\\&(0)(1)(2)(2)(2)(1)(2)(2)(2)=\varphi(\omega^{\omega^2},0)\\&(0)(1)(2)(2)(2)(2)=\varphi(\omega^{\omega^\omega},0)\\&(0)(1)(2)(3)=\varphi(\varphi(1,0),0)\\&(0)(1)(2)(3)(1)(2)=\varphi(\varphi(1,0)+1,0)\\&(0)(1)(2)(3)(1)(2)(1)(2)(3)=\varphi(\varphi(1,0)\times2,0)\\&(0)(1)(2)(3)(1)(2)(2)=\varphi(\omega^{\varphi(1,0)+1},0)\\&(0)(1)(2)(3)(1)(2)(2)(2)=\varphi(\omega^{\omega^{\varphi(1,0)+1}},0)\\&(0)(1)(2)(3)(1)(2)(3)=\varphi(\varphi(1,1),0)\\&(0)(1)(2)(3)(2)=\varphi(\varphi(1,\omega),0)\\&(0)(1)(2)(3)(2)(2)=\varphi(\varphi(1,\omega^\omega),0)\\&(0)(1)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,0)),0)\\&(0)(1)(2)(3)(2)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,\varphi(1,0))),0)\\&(0)(1)(2)(3)(2)(3)=\varphi(\varphi(2,0),0)\\&(0)(1)(2)(3)(2)(3)(2)(3)=\varphi(\varphi(3,0),0)\\&(0)(1)(2)(3)(3)=\varphi(\varphi(\omega,0),0)\\&(0)(1)(2)(3)(3)(2)(3)=\varphi(\varphi(\omega+1,0),0)\\&(0)(1)(2)(3)(3)(2)(3)(3)=\varphi(\varphi(\omega^2,0),0)\\&(0)(1)(2)(3)(3)(3)=\varphi(\varphi(\omega^\omega,0),0)\\&(0)(1)(2)(3)(4)=\varphi(\varphi(\varphi(1,0),0),0)\\&(0)(1)(2)(3)(4)(2)(3)(4)=\varphi(\varphi(\varphi(1,1),0),0)\\&(0)(1)(2)(3)(4)(3)(4)=\varphi(\varphi(\varphi(2,0),0),0)\\&(0)(1)(2)(3)(4)(4)=\varphi(\varphi(\varphi(\omega,0),0),0)\\&(0)(1)(2)(3)(4)(5)=\varphi(\varphi(\varphi(\varphi(1,0),0),0),0)\\&(0)(1)(2)(3)(4)(5)(6)=\varphi(\varphi(\varphi(\varphi(\varphi(1,0),0),0),0),0)\\&(0,0)(1,1)=\varphi(1,0,0) \end{aligned}</nowiki>
[[分类:分析]]

BHM分析Part1：0~FSO

2026-02-20T07:17:36Z

Baixie01000a7：

本条目展示[[BHM]]强度分析的第一部分。使用[[Veblen 函数|Veblen函数]]。

<nowiki>\begin{aligned} & \varnothing=0\\&(0)=1\\&(0)(0)=2\\&(0)(1)=\omega\\&(0)(1)(0)=\omega+1\\&(0)(1)(0)(0)=\omega+2\\&(0)(1)(0)(0)(1)=\omega\times2\\&(0)(1)(0)(0)(1)(0)=\omega\times2+1\\&(0)(1)(0)(0)(1)(0)(0)(1)=\omega\times3\\&(0)(1)(0)(1)=\omega^2\\&(0)(1)(0)(1)(0)=\omega^2+1\\&(0)(1)(0)(1)(0)(0)(1)=\omega^2+\omega\\&(0)(1)(0)(1)(0)(0)(1)(0)(0)(1)=\omega^2+\omega\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times3\\&(0)(1)(0)(1)(0)(1)=\omega^3\\&(0)(1)(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(1)=\omega^3\times2\\&(0)(1)(0)(1)(0)(1)(0)(1)=\omega^4\\&(0)(1)(1)=\omega^\omega\\&(0)(1)(1)(0)(0)(1)=\omega^\omega+\omega\\&(0)(1)(1)(0)(0)(1)(0)(1)=\omega^\omega+\omega^2\\&(0)(1)(1)(0)(0)(1)(1)=\omega^\omega\times2\\&(0)(1)(1)(0)(1)=\omega^{\omega+1}\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)=\omega^{\omega+1}+\omega^\omega\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)(0)(1)=\omega^{\omega+1}\times2\\&(0)(1)(1)(0)(1)(0)(1)=\omega^{\omega+2}\\&(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times2}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)=\omega^{\omega\times2+1}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times3}\\&(0)(1)(1)(0)(1)(1)=\omega^{\omega^2}\\&(0)(1)(1)(0)(1)(1)(0)(1)=\omega^{\omega^2+1}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega^2+\omega}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^2\times2}\\&(0)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^3}\\&(0)(1)(1)(1)=\omega^{\omega^\omega}\\&(0)(1)(1)(1)(0)(0)(1)(1)(1)=\omega^{\omega^\omega}\times2\\&(0)(1)(1)(1)(0)(1)=\omega^{\omega^\omega+1}\\&(0)(1)(1)(1)(0)(1)(0)(1)(1)(1)=\omega^{\omega^\omega\times2}\\&(0)(1)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+1}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+2}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega\times2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^3}}\\&(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^\omega}}\\&(0)(1)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^\omega}}}\\&(0)(1)(2)=\varepsilon_0\\&(0)(1)(2)(0)(0)(1)(2)=\varepsilon_0\times2\\&(0)(1)(2)(0)(1)=\omega^{\varepsilon_0+1}\\&(0)(1)(2)(0)(1)(0)(1)=\omega^{\varepsilon_0+2}\\&(0)(1)(2)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega\times2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega^2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)=\omega^{\varepsilon_0+\omega^\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)(1)=\omega^{\varepsilon_0+\omega^{\omega^\omega}}\\&(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times2}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)=\omega^{\varepsilon_0\times2+1}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times3}\\&(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(0)(1)(1)(0)(1)=\omega^{\omega^{\varepsilon_0+1}+1}\\&(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}\times2}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+2}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega^\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(2)=\omega^{\omega^{\varepsilon_0\times2}}\\&(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}\\&(0)(1)(2)(0)(1)(2)=\varepsilon_1\\&(0)(1)(2)(0)(1)(2)(0)(1)=\omega^{\varepsilon_1+1}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_1+\varepsilon_0}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_1\times2}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_1+1}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_1+1}}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(2)=\varepsilon_2\\&(0)(1)(2)(1)=\varepsilon_\omega\\&(0)(1)(2)(1)(0)(1)=\omega^{\varepsilon_\omega+1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_\omega+\varepsilon_1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(1)=\omega^{\varepsilon_\omega\times2}\\&(0)(1)(2)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_\omega+1}}\\&(0)(1)(2)(1)(0)(1)(2)=\varepsilon_{\omega+1}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)=\varepsilon_{\omega+2}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega\times2}\\&(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^2}\\&(0)(1)(2)(1)(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^3}\\&(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega}\\&(0)(1)(2)(1)(1)(0)(1)(2)=\varepsilon_{\omega^\omega+1}\\&(0)(1)(2)(1)(1)(0)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega\times2}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)=\varepsilon_{\omega^{\omega+1}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega\times2}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^2}}\\&(0)(1)(2)(1)(1)(1)=\varepsilon_{\omega^{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)=\varepsilon_{\varepsilon_0+1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_2}\\&(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_\omega}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\omega+1}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega\times2}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^2}}\\&(0)(1)(2)(1)(1)(2)(1)(1)=\varepsilon_{\varepsilon_{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(1)=\varepsilon_{\varepsilon_{\omega^{\omega^\omega}}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_1}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\varepsilon_\omega}}\\&(0)(1)(2)(1)(2)=\zeta_0\\&(0)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(0)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\zeta_0\times2}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0\times2}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_1\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_2\\&(0)(1)(2)(1)(2)(1)=\zeta_\omega\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)=\zeta_{\omega+1}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega\times2}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^2}\\&(0)(1)(2)(1)(2)(1)(1)=\zeta_{\omega^\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\varepsilon_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)=\zeta_{\varepsilon_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_{\varepsilon_0}}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_1}</nowiki><nowiki>\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)=\zeta_{\zeta_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\zeta_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_{\zeta_0}}\\&(0)(1)(2)(1)(2)(1)(2)=\eta_0\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(2)=\eta_1\\&(0)(1)(2)(1)(2)(1)(2)(1)=\eta_\omega\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)=\eta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\eta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(2)=\eta_{\eta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(4,0)\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(5,0)\\&(0)(1)(2)(2)=\varphi(\omega,0)\\&(0)(1)(2)(2)(0)(1)(2)=\varphi(1,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)=\varphi(2,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)(1)(2)=\varphi(3,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,1)\\&(0)(1)(2)(2)(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,2)\\&(0)(1)(2)(2)(1)=\varphi(\omega,\omega)\\&(0)(1)(2)(2)(1)(1)(2)=\varphi(\omega,\varphi(1,0))\\&(0)(1)(2)(2)(1)(1)(2)(1)(2)=\varphi(\omega,\varphi(2,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,\varphi(\omega,0)))\\&(0)(1)(2)(2)(1)(2)=\varphi(\omega+1,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)=\varphi(\omega+2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times3,0)\\&(0)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)=\varphi(\omega^2+1,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2\times2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^3,0)\\&(0)(1)(2)(2)(2)=\varphi(\omega^\omega,0)\\&(0)(1)(2)(2)(2)(1)(2)=\varphi(\omega^\omega+1,0)\\&(0)(1)(2)(2)(2)(1)(2)(2)=\varphi(\omega^{\omega+1},0)\\&(0)(1)(2)(2)(2)(1)(2)(2)(2)=\varphi(\omega^{\omega^2},0)\\&(0)(1)(2)(2)(2)(2)=\varphi(\omega^{\omega^\omega},0)\\&(0)(1)(2)(3)=\varphi(\varphi(1,0),0)\\&(0)(1)(2)(3)(1)(2)=\varphi(\varphi(1,0)+1,0)\\&(0)(1)(2)(3)(1)(2)(1)(2)(3)=\varphi(\varphi(1,0)\times2,0)\\&(0)(1)(2)(3)(1)(2)(2)=\varphi(\omega^{\varphi(1,0)+1},0)\\&(0)(1)(2)(3)(1)(2)(2)(2)=\varphi(\omega^{\omega^{\varphi(1,0)+1}},0)\\&(0)(1)(2)(3)(1)(2)(3)=\varphi(\varphi(1,1),0)\\&(0)(1)(2)(3)(2)=\varphi(\varphi(1,\omega),0)\\&(0)(1)(2)(3)(2)(2)=\varphi(\varphi(1,\omega^\omega),0)\\&(0)(1)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,0)),0)\\&(0)(1)(2)(3)(2)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,\varphi(1,0))),0)\\&(0)(1)(2)(3)(2)(3)=\varphi(\varphi(2,0),0)\\&(0)(1)(2)(3)(2)(3)(2)(3)=\varphi(\varphi(3,0),0)\\&(0)(1)(2)(3)(3)=\varphi(\varphi(\omega,0),0)\\&(0)(1)(2)(3)(3)(2)(3)=\varphi(\varphi(\omega+1,0),0)\\&(0)(1)(2)(3)(3)(2)(3)(3)=\varphi(\varphi(\omega^2,0),0)\\&(0)(1)(2)(3)(3)(3)=\varphi(\varphi(\omega^\omega,0),0)\\&(0)(1)(2)(3)(4)=\varphi(\varphi(\varphi(1,0),0),0)\\&(0)(1)(2)(3)(4)(2)(3)(4)=\varphi(\varphi(\varphi(1,1),0),0)\\&(0)(1)(2)(3)(4)(3)(4)=\varphi(\varphi(\varphi(2,0),0),0)\\&(0)(1)(2)(3)(4)(4)=\varphi(\varphi(\varphi(\omega,0),0),0)\\&(0)(1)(2)(3)(4)(5)=\varphi(\varphi(\varphi(\varphi(1,0),0),0),0)\\&(0)(1)(2)(3)(4)(5)(6)=\varphi(\varphi(\varphi(\varphi(\varphi(1,0),0),0),0),0)\\&(0,0)(1,1)=\varphi(1,0,0) \end{aligned}</nowiki>
[[分类:分析]]

PPS分析Part2

2026-02-20T07:14:06Z

Baixie01000a7：

{| class="wikitable"
! [[PPS]] !! [[康托范式]]
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,0,3,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,9)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,9,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,9,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,9,0,16,9,0,0,9,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,10)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,0,10,9,0,0,10)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^{\omega+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^{\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\omega^{\omega^{\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,0,3,0,17,16,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,0,3,0,20,19,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,0,3,0,20,19,0,23,19)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}\times3}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,9)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,9,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,0,13,9,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega^{\omega+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega^{\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega^{\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,9,0,13,9,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,15,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,15,0,19,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,15,0,19,15,0,0,15,0,25)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,15,0,19,15,0,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,15,0,19,15,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,3,0,10,10,3,0,3,0,16,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,13,0,17)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,13,0,17,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,13,0,17,13,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,3,0,14,14,3,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,0,4,3,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,0,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,0,21,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,0,22,21,0,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\omega+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,25)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,25,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,21,0,25,21,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,3,0,28,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,22,3,0,27)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,22,3,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,22,3,0,29,0,22,3,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}+\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,3,0,22,22,3,0,22,3,0,29,27)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,0,4,3,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}+\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34,3,0,34,3,0,41,39)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}+\omega^{\omega^{\varepsilon_0+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34,3,0,34,3,0,41,39,3,0,0,3,0,48,0,3,0,52,52,3,0,52,3,0,59,57)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}+\omega^{\omega^{\varepsilon_0+1}\times2}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34,3,0,34,3,0,41,39,3,0,0,3,0,48,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}+\omega^{\omega^{\varepsilon_0+1}\times2+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34,3,0,34,3,0,41,39,3,0,0,3,0,48,0,34,3,0,53)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}+\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,3,0,34,34,3,0,34,3,0,41,39,3,0,0,3,0,48,0,34,3,0,53,51)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,33)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times4}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33,3,0,0,3,0,42,0,3,0,46,46,3,0,46,3,0,53,51)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times4}+\omega^{\omega^{\varepsilon_0+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33,3,0,0,3,0,42,0,3,0,46,46,3,0,46,3,0,53,51,3,0,0,3,0,60,0,46,3,0,65,63)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times4}+\omega^{\omega^{\varepsilon_0+1}\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33,3,0,0,3,0,42,0,3,0,46,46,3,0,46,3,0,53,51,3,0,0,3,0,60,0,46,3,0,65,63,3,0,0,3,0,72,0,46,3,0,77,75)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times4}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33,3,0,0,3,0,42,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times4+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,0,4,3,0,23,21,3,0,0,3,0,30,0,4,3,0,35,33,3,0,0,3,0,42,0,4,3,0,47,45)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times5}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,28,0,32)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,0,3,0,47,47,3,0,47,3,0,54,52)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}\times2}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}\times2+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,0,29,3,0,48)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,0,29,3,0,48,46)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}+\omega^{\omega^{\varepsilon_0+1}\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,3,0,29,29,3,0,29,3,0,36,34,3,0,0,3,0,43,34,3,0,0,3,0,50,0,3,0,54,54,3,0,54,3,0,61,59,3,0,0,3,0,68,59)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}}\times3}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,4,3,0,30,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}+\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,4,3,0,30,28,3,0,0,3,0,37,0,4,3,0,42,40)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}+\omega^{\varepsilon_0+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,4,3,0,30,28,3,0,0,3,0,37,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,0,4,3,0,30,28,3,0,0,3,0,37,28,3,0,0,3,0,44,0,4,3,0,49,47,3,0,0,3,0,56,47)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+2}\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,3,0,18,9,3,0,0,3,0,25,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+3}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,0,4,3,0,21,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega}+\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,0,4,3,0,21,19,3,0,0,3,0,28,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega}+\omega^{\varepsilon_0+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,0,4,3,0,21,19,3,0,0,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,3,0,23,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,3,0,23,9,3,0,0,3,0,30,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega+3}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,3,0,23,9,3,0,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,3,0,23,9,3,0,0,23,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega\times2+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,3,0,23,9,3,0,0,23,9,3,0,0,3,0,35,9,3,0,0,35,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega\times3+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,11,9,3,0,0,3,0,28,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^2+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,11,9,3,0,0,3,0,28,9,3,0,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^2+\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,11,9,3,0,0,3,0,28,9,3,0,0,28,9,3,0,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^2\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,0,11,9,3,0,0,11,9,3,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^3}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,3,0,22,9,3,0,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega+\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,3,0,22,9,3,0,0,22,9,3,0,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega+\omega^2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,3,0,22,9,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,11,9,3,0,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,0,11,9,3,0,21,9,3,0,0,11,9,3,0,30)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega\times3}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega^2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,12,9,3,0,12,9,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega^3}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+\omega^{\omega^\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,3,0,20,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0\times2+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,3,0,20,9,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0\times3}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,11,9,3,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,11,9,3,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,11,9,3,0,21)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,0,11,9,3,0,21,0,0,11,9,3,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times3}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,0,11,9,3,0,24)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,0,11,9,3,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,0,11,9,3,0,26,0,0,11,9,3,0,33)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,0,11,9,3,0,26,0,24)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,12,9,3,0,0,0,11,9,3,0,31,0,29,9,3,0,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+2}\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,0,12,9,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+3}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,12,9,3,0,20,0,12,9,3,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times3}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,0,12,9,3,0,31)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22,9,3,0,0,0,12,9,3,0,36,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22,9,3,0,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22,9,3,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22,9,3,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,22,9,3,0,30)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\varepsilon_0}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34,0,0,12,9,3,0,41)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\varepsilon_0\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34,0,32)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34,0,32,9,3,0,0,32)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34,0,32,9,3,0,40)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0\times2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,12,9,3,0,24,0,23,3,0,0,12,9,3,0,34,0,33)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\varepsilon_0}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,26,9,3,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0\times2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,0,12,9,3,0,39,0,38)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,0,0,12,9,3,0,44,0,43,3,0,0,42)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}+1}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,0,26,9,3,0,0,0,12,9,3,0,49,0,48,3,0,0,47,9,3,0,0,47)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+2}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,0,26,9,3,0,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+3}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,36)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\omega}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,0,26,9,3,0,45)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,36)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+\omega^{\varepsilon_0+1}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,36,9,3,0,0,36)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+2}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,36,9,3,0,42)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,36,9,3,0,44)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times2}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,36,9,3,0,44,0,36,9,3,0,50)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0\times3}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,37)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,26,9,3,0,38,0,37,3,0,0,26,9,3,0,48,0,47)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}\times2}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,27)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,12,9,3,0,28,0,27,3,0,0,27,3,0,0,12,9,3,0,42,0,41,3,0,0,41)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,0,13,3,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18)</math> || <math>\varepsilon_{\varepsilon_1}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3)</math> || <math>\varepsilon_{\omega^{\varepsilon_1+1}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27)</math> || <math>\varepsilon_{\omega^{\varepsilon_1+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,3,0,31,31,3,0,31,3,0,38,36,3,0,41,0,40,3,0,45)</math> || <math>\varepsilon_{\omega^{\varepsilon_1\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_1+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_1+2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,4,3,0,31)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_1+\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,4,3,0,32)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_1+\varepsilon_0}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,0,4,3,0,32,30,3,0,35,0,34,3,0,39)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_1\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_1+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,9,3,0,0,3,0,34,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_1+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,9,3,0,0,27)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_1+\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,9,3,0,30)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_1+\varepsilon_0}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,3,0,27,9,3,0,30,0,29,3,0,34)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_1\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_1+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,0,11,9,3,0,28,0,27,3,0,32)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_1\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_1+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,12,9,3,0,27,0,26,3,0,31)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_1\times2}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^{\varepsilon_1+1}}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,13,3,0,25)</math> || <math>\varepsilon_{\varepsilon_2}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,0,13,3,0,25,3,0,0,13,3,0,32)</math> || <math>\varepsilon_{\varepsilon_3}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,18,3,0,18)</math> || <math>\varepsilon_{\varepsilon_\omega}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,19)</math> || <math>\varepsilon_{\varepsilon_{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,13,3,0,19,0,13,3,0,24)</math> || <math>\varepsilon_{\varepsilon_{\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,14)</math> || <math>\varepsilon_{\varepsilon_{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,14,0,14,0,14)</math> || <math>\varepsilon_{\varepsilon_{\omega^{\omega^{\omega+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15)</math> || <math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,0,3)</math> || <math>\varepsilon_{\omega^{\varepsilon_{\varepsilon_0}+1}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,0,3,0,22,9)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,0,15,9,3,0,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega^2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\varepsilon_0}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega^{\varepsilon_0+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,17)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega^{\omega^{\varepsilon_0+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,17,3,0,0,17)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,17,3,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\varepsilon_1}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,17,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\varepsilon_{\omega^\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\varepsilon_{\omega^{\omega+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,18,0,18,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+\varepsilon_{\omega^{\omega^{\omega+1}+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,9,3,0,15,9,3,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,4,3,0,4,3,0,11,10)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}</math>
|-

[[分类:分析]]

PPS分析Part1

2026-02-20T07:12:21Z

Baixie01000a7：

{| class="wikitable"
! [[PPS]] !! [[康托范式]]
|-
| <math>(0,1)</math> || <math>\omega</math>
|-
| <math>(0,1,0,0,3)</math> || <math>\omega\times2</math>
|-
| <math>(0,1,0,0,3,0,0,6)</math> || <math>\omega\times3</math>
|-
| <math>(0,1,0,0,3,0,0,6,0,0,9)</math> || <math>\omega\times4</math>
|-
| <math>(0,1,0,0,3,3)</math> || <math>\omega^2</math>
|-
| <math>(0,1,0,0,3,3,0,0,7)</math> || <math>\omega^2+\omega</math>
|-
| <math>(0,1,0,0,3,3,0,0,7,0,0,10)</math> || <math>\omega^2+\omega\times2</math>
|-
| <math>(0,1,0,0,3,3,0,0,7,7)</math> || <math>\omega^2\times2</math>
|-
| <math>(0,1,0,0,3,3,0,0,7,7,0,0,11,11)</math> || <math>\omega^2\times3</math>
|-
| <math>(0,1,0,0,3,3,3)</math> || <math>\omega^3</math>
|-
| <math>(0,1,0,0,3,3,3,0,0,8,8)</math> || <math>\omega^3+\omega^2</math>
|-
| <math>(0,1,0,0,3,3,3,0,0,8,8,8)</math> || <math>\omega^3\times2</math>
|-
| <math>(0,1,0,0,3,3,3,3)</math> || <math>\omega^4</math>
|-
| <math>(0,1,0,0,4)</math> || <math>\omega^\omega</math>
|-
| <math>(0,1,0,0,4,0,0,6)</math> || <math>\omega^\omega+\omega</math>
|-
| <math>(0,1,0,0,4,0,0,6,6)</math> || <math>\omega^\omega+\omega^2</math>
|-
| <math>(0,1,0,0,4,0,0,7)</math> || <math>\omega^\omega\times2</math>
|-
| <math>(0,1,0,0,4,0,0,7,0,0,9)</math> || <math>\omega^\omega\times2+\omega</math>
|-
| <math>(0,1,0,0,4,0,0,7,0,0,10)</math> || <math>\omega^\omega\times3</math>
|-
| <math>(0,1,0,1)</math> || <math>\omega^{\omega+1}</math>
|-
| <math>(0,1,0,1,0,0,5)</math> || <math>\omega^{\omega+1}+\omega</math>
|-
| <math>(0,1,0,1,0,0,5,0,0,8)</math> || <math>\omega^{\omega+1}+\omega\times2</math>
|-
| <math>(0,1,0,1,0,0,5,5)</math> || <math>\omega^{\omega+1}+\omega^2</math>
|-
| <math>(0,1,0,1,0,0,6)</math> || <math>\omega^{\omega+1}+\omega^\omega</math>
|-
| <math>(0,1,0,1,0,0,6,0,0,8)</math> || <math>\omega^{\omega+1}+\omega^\omega+\omega</math>
|-
| <math>(0,1,0,1,0,0,6,0,0,9)</math> || <math>\omega^{\omega+1}+\omega^\omega\times2</math>
|-
| <math>(0,1,0,1,0,0,6,0,6)</math> || <math>\omega^{\omega+1}\times2</math>
|-
| <math>(0,1,0,1,0,0,6,0,6,0,0,11,0,11)</math> || <math>\omega^{\omega+1}\times3</math>
|-
| <math>(0,1,0,1,0,1)</math> || <math>\omega^{\omega+2}</math>
|-
| <math>(0,1,0,1,0,1,0,0,8)</math> || <math>\omega^{\omega+2}+\omega^\omega</math>
|-
| <math>(0,1,0,1,0,1,0,0,8,0,8)</math> || <math>\omega^{\omega+2}+\omega^{\omega+1}</math>
|-
| <math>(0,1,0,1,0,1,0,0,8,0,8,0,8)</math> || <math>\omega^{\omega+2}\times2</math>
|-
| <math>(0,1,0,1,0,1,0,1)</math> || <math>\omega^{\omega+3}</math>
|-
| <math>(0,1,0,2)</math> || <math>\omega^{\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,0,6)</math> || <math>\omega^{\omega\times2}+\omega</math>
|-
| <math>(0,1,0,2,0,0,0,6,0,0,9)</math> || <math>\omega^{\omega\times2}+\omega2</math>
|-
| <math>(0,1,0,2,0,0,0,6,6)</math> || <math>\omega^{\omega\times2}+\omega^2</math>
|-
| <math>(0,1,0,2,0,0,0,7)</math> || <math>\omega^{\omega\times2}+\omega^\omega</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,0,10)</math> || <math>\omega^{\omega\times2}+\omega^\omega\times2</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,7)</math> || <math>\omega^{\omega\times2}+\omega^{\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,7,0,7)</math> || <math>\omega^{\omega\times2}+\omega^{\omega+2}</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,8)</math> || <math>\omega^{\omega\times2}\times2</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,8,0,0,0,13)</math> || <math>\omega^{\omega\times2}\times2+\omega^\omega</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,8,0,0,0,13,0,13)</math> || <math>\omega^{\omega\times2}\times2+\omega^{\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,0,7,0,8,0,0,0,13,0,14)</math> || <math>\omega^{\omega\times2}\times3</math>
|-
| <math>(0,1,0,2,0,0,1)</math> || <math>\omega^{\omega\times2+1}</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,0,10)</math> || <math>\omega^{\omega\times2+1}+\omega^\omega</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,0,10,0,10)</math> || <math>\omega^{\omega\times2+1}+\omega^{\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,0,10,0,11)</math> || <math>\omega^{\omega\times2+1}+\omega^{\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,0,10,0,11,0,0,10)</math> || <math>\omega^{\omega\times2+1}\times2</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,1)</math> || <math>\omega^{\omega\times2+2}</math>
|-
| <math>(0,1,0,2,0,0,1,0,0,1,0,0,1)</math> || <math>\omega^{\omega\times2+3}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6)</math> || <math>\omega^{\omega\times3}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,0,1)</math> || <math>\omega^{\omega\times3+1}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,0,1,0,11)</math> || <math>\omega^{\omega\times4}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,6)</math> || <math>\omega^{\omega^2}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,6,0,0,1)</math> || <math>\omega^{\omega^2+1}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,6,0,0,1,0,13)</math> || <math>\omega^{\omega^2+\omega}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,6,0,0,1,0,13,0,13)</math> || <math>\omega^{\omega^2\times2}</math>
|-
| <math>(0,1,0,2,0,0,1,0,6,0,6,0,6)</math> || <math>\omega^{\omega^3}</math>
|-
| <math>(0,1,0,2,0,0,1,0,7)</math> || <math>\omega^{\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,1,0,7,0,0,1)</math> || <math>\omega^{\omega^\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,1,0,7,0,0,1,0,11)</math> || <math>\omega^{\omega^\omega+\omega}</math>
|-
| <math>(0,1,0,2,0,0,1,0,7,0,0,1,0,11,0,11)</math> || <math>\omega^{\omega^\omega+\omega^2}</math>
|-
| <math>(0,1,0,2,0,0,1,0,7,0,0,1,0,11,0,12)</math> || <math>\omega^{\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2)</math> || <math>\omega^{\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1)</math> || <math>\omega^{\omega^{\omega+1}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,9)</math> || <math>\omega^{\omega^{\omega+1}+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,9,0,9)</math> || <math>\omega^{\omega^{\omega+1}+\omega^2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10)</math> || <math>\omega^{\omega^{\omega+1}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,0,1,0,15)</math> || <math>\omega^{\omega^{\omega+1}+\omega^\omega+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,0,1,0,16)</math> || <math>\omega^{\omega^{\omega+1}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9)</math> || <math>\omega^{\omega^{\omega+1}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,0,1,0,18)</math> || <math>\omega^{\omega^{\omega+1}\times2+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,0,1,0,19)</math> || <math>\omega^{\omega^{\omega+1}\times2+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,0,1,0,19,0,0,0,1,0,25)</math> || <math>\omega^{\omega^{\omega+1}\times2+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,0,1,0,19,0,0,18)</math> || <math>\omega^{\omega^{\omega+1}\times3}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9)</math> || <math>\omega^{\omega^{\omega+2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1)</math> || <math>\omega^{\omega^{\omega+2}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,21)</math> || <math>\omega^{\omega^{\omega+2}+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22)</math> || <math>\omega^{\omega^{\omega+2}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,0,1,0,28)</math> || <math>\omega^{\omega^{\omega+2}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,21)</math> || <math>\omega^{\omega^{\omega+2}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,21,0,0,0,1,0,31)</math> || <math>\omega^{\omega^{\omega+2}+\omega^{\omega+1}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,21,0,0,0,1,0,31,0,0,30)</math> || <math>\omega^{\omega^{\omega+2}+\omega^{\omega+1}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,21,0,0,21)</math> || <math>\omega^{\omega^{\omega+2}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,0,1,0,22,0,0,21,0,0,21,0,0,0,1,0,34,0,0,33,0,0,33)</math> || <math>\omega^{\omega^{\omega+2}\times3}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,0,9,0,0,9)</math> || <math>\omega^{\omega^{\omega+3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,14)</math> || <math>\omega^{\omega^{\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,14,0,0,9)</math> || <math>\omega^{\omega^{\omega\times2+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,14,0,0,9,0,19)</math> || <math>\omega^{\omega^{\omega\times3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,14,0,14)</math> || <math>\omega^{\omega^{\omega^2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,14,0,14,0,14)</math> || <math>\omega^{\omega^{\omega^3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,15)</math> || <math>\omega^{\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,15,0,0,9)</math> || <math>\omega^{\omega^{\omega^\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,15,0,0,9,0,19)</math> || <math>\omega^{\omega^{\omega^\omega+\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,9,0,15,0,0,9,0,20)</math> || <math>\omega^{\omega^{\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,17)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,0,1,0,24)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,0,1,0,24,0,0,0,1,0,30)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega\times3}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,17)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,17,0,0,17)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega+2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,17,0,22)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,17,0,23)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,17,0,23,0,0,17,0,28)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,1,0,10,0,0,10,0,0,1,0,18,0,0,18)</math> || <math>\omega^{\omega^{\omega^{\omega+1}}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^\omega+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,0,1,0,18)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^\omega+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,0,1,0,19)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,12,0,17)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,12,0,18)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,12,0,18,0,0,12,0,23)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,21)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22,0,0,0,1,0,28)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22,0,0,21)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22,0,0,21,0,26)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega^{\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22,0,0,21,0,27)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,0,1,0,22,0,0,22)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}+\omega^{\omega^{\omega+1}}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,0,0,1,0,25,0,0,25)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}\times2+\omega^{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,0,0,1,0,25,0,0,25,0,0,24)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+1}\times3}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,0,12,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,20)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega^\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,0,12,0,26)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega^\omega+\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,0,12,0,27)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,0,12,0,27,0,0,0,12,0,33)</math> || <math>\omega^{\omega^{\omega^{\omega+1}+\omega^\omega\times3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20)</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times2+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,0,12,0,30)</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times2+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,0,12,0,30,0,0,0,12,0,36 )</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times2+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,0,12,0,30,0,0,29)</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times3}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,0,12,0,30,0,0,29,0,0,0,12,0,39,0,0,38 )</math> || <math>\omega^{\omega^{\omega^{\omega+1}\times4}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,20)</math> || <math>\omega^{\omega^{\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,20,0,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega+2}+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,20,0,0,0,12,0,33,0,0,32)</math> || <math>\omega^{\omega^{\omega^{\omega+2}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,20,0,0,0,12,0,33,0,0,32,0,0,32)</math> || <math>\omega^{\omega^{\omega^{\omega+2}\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,0,20,0,0,20)</math> || <math>\omega^{\omega^{\omega^{\omega+3}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,25)</math> || <math>\omega^{\omega^{\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,25,0,0,20)</math> || <math>\omega^{\omega^{\omega^{\omega\times2+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,25,0,0,20,0,30)</math> || <math>\omega^{\omega^{\omega^{\omega\times3}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,25,0,25)</math> || <math>\omega^{\omega^{\omega^{\omega^2}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,26)</math> || <math>\omega^{\omega^{\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,20,0,26,0,0,20,0,31)</math> || <math>\omega^{\omega^{\omega^{\omega^\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+1}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30,0,0,29)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30,0,0,29,0,35)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30,0,0,30)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+\omega^{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30,0,0,30,0,0,29)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}+\omega^{\omega^{\omega+1}+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,0,1,0,30,0,0,30,0,0,29,0,38,0,0,38)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}+1}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12,0,29)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12,0,29,0,0,28)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12,0,29,0,0,28,0,33)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12,0,29,0,0,28,0,34)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,12,0,21,0,0,21,0,0,12,0,29,0,0,29)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}}\times2}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,13)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,1,0,13,0,0,13,0,0,13,0,0,1,0,24,0,0,24,0,0,24)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}+1}}\times2}</math>
|-
| <math>(0,1,0,2,0,0,2,0,0,2,0,0,2)</math> || <math>\omega^{\omega^{\omega^{\omega^{\omega+1}+1}+1}}</math>
|-
| <math>(0,1,0,2,0,3)</math> || <math>\varepsilon _0</math>
|-
| <math>(0,1,0,2,0,3,0,0,1)</math> || <math>\omega^{\varepsilon_0+1}</math>
|-
| <math>(0,1,0,2,0,3,0,0,1,0,9)</math> || <math>\omega^{\varepsilon_0+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,3,0,0,1,0,9,0,10)</math> || <math>\omega^{\varepsilon_0\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,1,0,9,0,10,0,0,1,0,16,0,17)</math> || <math>\omega^{\varepsilon_0\times3}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2)</math> || <math>\omega^{\omega^{\varepsilon_0+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13)</math> || <math>\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,0,1,0,20,0,21)</math> || <math>\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11)</math> || <math>\omega^{\omega^{\varepsilon_0+1}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,0,1,0,23,0,24)</math> || <math>\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,0,1,0,23,0,24,0,0,0,1,0,31,0,32)</math> || <math>\omega^{\omega^{\varepsilon_0+1}\times2+\varepsilon_0\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,0,1,0,23,0,24,0,0,22)</math> || <math>\omega^{\omega^{\varepsilon_0+1}\times3}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,0,1,0,23,0,24,0,0,22,0,0,0,1,0,34,0,35,0,0,33)</math> || <math>\omega^{\omega^{\varepsilon_0+1}\times4}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,11)</math> || <math>\omega^{\omega^{\varepsilon_0+2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,11,0,0,0,1,0,26,0,27,0,0,25,0,0,25)</math> || <math>\omega^{\omega^{\varepsilon_0+2}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,0,11,0,0,11)</math> || <math>\omega^{\omega^{\varepsilon_0+3}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,18)</math> || <math>\omega^{\omega^{\varepsilon_0+\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,19)</math> || <math>\omega^{\omega^{\varepsilon_0+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,19,0,20)</math> || <math>\omega^{\omega^{\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,19,0,20,0,0,11)</math> || <math>\omega^{\omega^{\varepsilon_0\times2+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,11,0,19,0,20,0,0,11,0,26,0,27)</math> || <math>\omega^{\omega^{\varepsilon_0\times3}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21,0,0,0,1,0,33,0,34,0,0,32)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+1}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21,0,0,21)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21,0,28)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21,0,29)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,21,0,29,0,30)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,1,0,12,0,13,0,0,12,0,0,1,0,22,0,23,0,0,22)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,14)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,14,0,0,14)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0+2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,14,0,22)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,14,0,22,0,23)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,0,1,0,26,0,27,0,0,26)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+\omega^{\omega^{\varepsilon_0+1}}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+1}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,0,14)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,0,14,0,33,0,34 )</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24,0,0,0,14,0,36,0,37,0,0,35 )</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+1}\times3}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24,0,0,24)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+2}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24,0,31)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+\omega}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24,0,32)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0+\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,24,0,32,0,33)</math> || <math>\omega^{\omega^{\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25,0,0,14)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25,0,0,14,0,35,0,36)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\varepsilon_0}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25,0,0,14,0,35,0,36,0,0,34)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25,0,0,14,0,35,0,36,0,0,34,0,42,0,43)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}+\omega^{\varepsilon_0\times2}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,14,0,25,0,26,0,0,25,0,0,14,0,35,0,36,0,0,35)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,1,0,15,0,16,0,0,15,0,0,15)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,0,2,0,0,2)</math> || <math>\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}+1}+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8)</math> || <math>\varepsilon_1</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,1)</math> || <math>\omega^{\varepsilon_1+1}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,1,0,14,0,15)</math> || <math>\omega^{\varepsilon_1+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,1,0,14,0,15,0,0,14,0,20)</math> || <math>\omega^{\varepsilon_1\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,1,0,14,0,15,0,0,14,0,20,0,0,1,0,26,0,27,0,0,26,0,32)</math> || <math>\omega^{\varepsilon_1\times3}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,2)</math> || <math>\omega^{\omega^{\varepsilon_1+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,2,0,13)</math> || <math>\varepsilon_2</math>
|-
| <math>(0,1,0,2,0,3,0,0,2,0,8,0,0,2,0,13,0,0,2,0,18)</math> || <math>\varepsilon_3</math>
|-
| <math>(0,1,0,2,0,3,0,3)</math> || <math>\varepsilon_\omega</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,1,0,11,0,12)</math> || <math>\omega^{\varepsilon_\omega+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,1,0,11,0,12,0,12)</math> || <math>\omega^{\varepsilon_\omega\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2)</math> || <math>\omega^{\omega^{\varepsilon_\omega+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10)</math> || <math>\varepsilon_{\omega+1}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17)</math> || <math>\omega^{\varepsilon_{\omega+1}+\varepsilon_\omega}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega+1}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15,0,0,0,1,0,29,0,30,0,30)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega+1}+\varepsilon_\omega}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15,0,0,0,1,0,29,0,30,0,30,0,0,28)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega+1}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15,0,0,15)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega+2}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15,0,25)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,15,0,25,0,26,0,26)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\varepsilon_\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,16)</math> || <math>\omega^{\varepsilon_{\omega+1}+\omega^{\omega^{\varepsilon_\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,1,0,16,0,17,0,17,0,0,16,0,24)</math> || <math>\omega^{\varepsilon_{\omega+1}\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,2)</math> || <math>\omega^{\omega^{\varepsilon_{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,0,2,0,15)</math> || <math>\varepsilon_{\omega+2}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,10)</math> || <math>\varepsilon_{\omega\times2}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,0,2,0,10,0,10,0,0,2,0,17,0,17)</math> || <math>\varepsilon_{\omega\times3}</math>
|-
| <math>(0,1,0,2,0,3,0,3,0,3)</math> || <math>\varepsilon_{\omega^2}</math>
|-
| <math>(0,1,0,2,0,4)</math> || <math>\varepsilon_{\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,4,0,1)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+1}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,0,0,1,0,14)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,0,7)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,0,7,0,0,7)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\omega^{\omega+2}}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,0,7,0,13)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,9)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,9,0,0,8,0,14)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\varepsilon_1}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,9,0,9)</math> || <math>\omega^{\varepsilon_{\omega^\omega}+\varepsilon_\omega}</math>
|-
| <math>(0,1,0,2,0,4,0,1,0,8,0,10)</math> || <math>\omega^{\varepsilon_{\omega^\omega}\times2}</math>
|-
| <math>(0,1,0,2,0,4,0,2)</math> || <math>\omega^{\omega^{\varepsilon_{\omega^\omega}+1}}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,7)</math> || <math>\varepsilon_{\omega^\omega+1}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,7,0,0,2,0,12)</math> || <math>\varepsilon_{\omega^\omega+2}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,7,0,7)</math> || <math>\varepsilon_{\omega^\omega+\omega}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,8)</math> || <math>\varepsilon_{\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,8,0,2,0,11)</math> || <math>\varepsilon_{\omega^\omega\times2+1}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,8,0,2,0,11,0,11)</math> || <math>\varepsilon_{\omega^\omega\times2+\omega}</math>
|-
| <math>(0,1,0,2,0,4,0,2,0,8,0,2,0,12)</math> || <math>\varepsilon_{\omega^\omega\times3}</math>
|-
| <math>(0,1,0,2,0,4,3)</math> || <math>\varepsilon_{\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,1)</math> || <math>\omega^{\varepsilon_{\omega^{\omega+1}}+1}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,2,0,10)</math> || <math>\varepsilon_{\omega^{\omega+1}+1}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,2,0,11)</math> || <math>\varepsilon_{\omega^{\omega+1}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,2,0,11,0,2,0,15)</math> || <math>\varepsilon_{\omega^{\omega+1}+\omega^\omega\times2}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,2,0,11,10)</math> || <math>\varepsilon_{\omega^{\omega+1}\times2}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,0,2,0,11,10,0,0,0,2,0,18,17)</math> || <math>\varepsilon_{\omega^{\omega+1}\times3}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3)</math> || <math>\varepsilon_{\omega^{\omega+2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,0,0,2,0,14)</math> || <math>\varepsilon_{\omega^{\omega+2}+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,0,0,2,0,14,13)</math> || <math>\varepsilon_{\omega^{\omega+2}+\omega^{\omega+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,0,0,2,0,14,13,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega+2}\times2}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,0,3)</math> || <math>\varepsilon_{\omega^{\omega+3}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,9)</math> || <math>\varepsilon_{\omega^{\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,10)</math> || <math>\varepsilon_{\omega^{\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,10,3)</math> || <math>\varepsilon_{\omega^{\omega^\omega+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,3,0,10,3,0,0,3,0,16)</math> || <math>\varepsilon_{\omega^{\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+1}+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,3,0,14 )</math> || <math>\varepsilon_{\omega^{\omega^{\omega+1}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,3,0,14,3,0,0,3,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+1}+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,3,0,14,3,0,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,4,3)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+2}+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,4,3,0,0,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+2}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,4,3,0,0,3,0,18,3,0,0,18,3,0,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+2}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,0,4,3,0,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega+3}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13,3,0,0,3,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}+\omega^\omega\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13,3,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13,3,0,0,13,3,0,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}+\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13,3,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,3,0,13,3,0,14,3,0,0,3,0,22,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2}\times3}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times2+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,4,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,0,4,3,0,12,3,0,0,4,3,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega\times4}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,5,3,0,0,4,3,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^2+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,5,3,0,0,4,3,0,15,3,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^2\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,5,3,0,5,3,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^3}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,3)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,3,0,12,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,3,0,12,3,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}+\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,3,0,12,3,0,14)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,11,3,0,0,4,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega+\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,11,3,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega+\omega^2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,0,4,3,0,12,0,0,4,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^\omega\times3}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,0,4)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,0,4,3,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}+\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,0,4,3,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}+\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,0,4,3,0,16,0,0,4,3,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}+\omega^\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,0,4,3,0,16,0,15)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+1}\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega+2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,10)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,11)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,11,0,5)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^\omega+1}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,5,3,0,11,0,5,3,0,16)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega+1}+\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega+1}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,0,0,5,3,0,23,0,22)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega+1}\times3}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega+2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,17)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,0,0,5,3,0,34,0,33)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega+1}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega+2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,0,23,3,0,0,0,5,3,0,38,0,37,3,0,0,37)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega+2}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,0,23,3,0,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega+3}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,28)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}+\omega^{\omega\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,29)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,0,5,3,0,24,0,23,3,0,29,0,0,5,3,0,35,0,34,3,0,40)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega}\times3}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,12)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,12,3,0,18,0,12,3,0,23)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^\omega\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,0,5,3,0,26)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^\omega\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,19,3,0,25)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,19,3,0,25,0,19)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,19,3,0,25,0,19,3,0,30)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}+\omega^{\omega^\omega\times2}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,5,3,0,13,0,13,0,5,3,0,20,0,20)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}}\times2}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,6,0,6,0,6)</math> || <math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega+1}+1}}}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7)</math> || <math>\varepsilon_{\varepsilon_0}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,0,2)</math> || <math>\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,0,2,0,10)</math> || <math>\varepsilon_{\varepsilon_0+1}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,0,2,0,11)</math> || <math>\varepsilon_{\varepsilon_0+\omega^\omega}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,0,2,0,11,10,0,14)</math> || <math>\varepsilon_{\varepsilon_0\times2}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+1}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,0,3,0,13)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^\omega}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,0,7)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^{\omega+1}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,0,7,3,0,0,3,0,17,3,0,0,17)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^{\omega+1}\times2}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,0,7,3,0,0,7)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^{\omega+2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,8)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^{\omega\times2}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,9)</math> || <math>\varepsilon_{\omega^{\varepsilon_0+\omega^{\omega^\omega}}}</math>
|-
| <math>(0,1,0,2,0,4,3,0,7,3,0,10)</math> || <math>\varepsilon_{\omega^{\varepsilon_0\times2}}</math>
|-
| <math>(0,1,0,2,0,4,4)</math> || <math>\varepsilon_{\omega^{\omega^{\varepsilon_0+1}}}</math>
|-

[[分类:分析]]