序数表

本条目列举出一些有名字的序数，它们大多在 googology 中具有重大意义。

需要注意的是，它们的命名很多来自 googology 爱好者而非专业数学研究者。

序数表

缩写	英文全称	常规表示方法（BOCF 等）	BMS / Y
FTO	First Transfinite Ordinal	$\omega$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1)$
LAO	Linear Array Ordinal	${\omega }^{\omega }$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1)(2)$
SCO	Small Cantor Ordinal	$\phi (1,0)={\epsilon }_0=\psi (\mathrm{\Omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)$
CO	Cantor Ordinal	$\phi (2,0)={\zeta }_0=\psi ({\mathrm{\Omega }}^2)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)$
LCO	Large Cantor Ordinal	$\phi (3,0)={\eta }_0=\psi ({\mathrm{\Omega }}^3)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(2,1)$
HCO	Hyper Cantor Ordinal	$\phi (\omega ,0)=\psi ({\mathrm{\Omega }}^{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(3,0)$
FSO	Feferman-Schütte Ordinal	$\phi (1,0,0)={\mathrm{\Gamma }}_0=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(3,1)$
ACO	Ackermann Ordinal	$\phi (1,0,0,0)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^2})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(3,1)(3,1)$
SVO	Small Veblen Ordinal	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\omega }})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(3,1)(4,0)$
LVO	Large Veblen Ordinal	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,1)(3,1)(4,1)$
BHO	Bachmann-Howard Ordinal	$\psi ({\mathrm{\Omega }}_2)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0)(1,1)(2,2)$
BO	Buchholz's Ordinal	$\psi ({\mathrm{\Omega }}_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)$
TFBO	Takeuti-Feferman-Buchholz Ordinal	$\psi ({\mathrm{\Omega }}_{\omega +1})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,0)(3,2,0)$
BIO	Bird's Ordinal	$\psi ({\mathrm{\Omega }}_{\mathrm{\Omega }})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,0)$
EBO	Extended Buchholz Ordinal	$\psi (I)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)$
JO	Jager's Ordinal	$\psi ({\mathrm{\Omega }}_{I+1})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)$
SIO	Small Inaccessible Ordinal	$\psi (I_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)$
MBO	Mutiply Buchholz Ordinal	$\psi (I(\omega ,0))=\psi (M^{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)$
TBO	Transfinitary Buchholz's Ordinal	$\psi (I(1,0,0))=\psi (M^M)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)$
SRO	Small Rathjen Ordinal	$\psi ({\epsilon }_{M+1})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)$
SMO	Small Mahlo Ordinal	$\psi (M_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)$
SNO	Small 1-Mahlo (N) Ordinal	$\psi (N_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)$
RO	Rathjen's Ordinal	$\psi ({\epsilon }_{K+1})$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0)$
SKO	Small Weakly Compact (K) Ordinal	$\psi (K_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)$
DO	Duchhart's Ordinal	$\psi (2\mathrm{a}\mathrm{f}\mathrm{t}\mathrm{4}\mathrm{)}$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,0)(6,2,0)$
SSO	Small Stegert Ordinal	$\psi (psd.{\mathrm{\Pi }}_{\omega })=\psi (a_2)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,0)$
LSO	Large Stegert Ordinal	$\psi (\lambda \alpha .(\alpha \times 2)-{\mathrm{\Pi }}_0)=\psi (a_2^a)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,0)(2,0,0)$
APO	Admissible-parameter free effective cardinal Ordinal	$\psi (\lambda \alpha .({\mathrm{\Omega }}_{\alpha +1})-{\mathrm{\Pi }}_1)=\psi (a_2^{{\mathrm{\Omega }}_{a+1}}+{\psi }_{a_2}(a_2^{{\mathrm{\Omega }}_{a+1}})\times \omega )$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,1)$
BGO	TSS 1st Back Gear Ordinal (CN ggg)	$\psi (\lambda \alpha .({\mathrm{\Omega }}_{\alpha +2})-{\mathrm{\Pi }}_1)=\psi ({\mathrm{\Omega }}_{a_2+1}+{\psi }_{a_2}({\mathrm{\Omega }}_{a_2+1})\times \omega )$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,1)$
SDO	Small Dropping Ordinal	$\psi (\lambda \alpha .({\mathrm{\Omega }}_{\alpha +\omega })-{\mathrm{\Pi }}_0=\psi ({\mathrm{\Omega }}_{a_2+1}\times \omega )$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,1)(3,0,0)$
LDO	Large Dropping Ordinal	$\psi (\lambda \alpha .({\psi }_{I_{\alpha +1}}(0))-{\mathrm{\Pi }}_0)=\psi ({\mathrm{\Omega }}_{a_2+1}\times a_2)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,1)(3,2,0)$
DSO	Doubly +1 Stable Ordinal	$\psi (\lambda \alpha .(\lambda \beta .\beta +1-{\mathrm{\Pi }}_0)-{\mathrm{\Pi }}_0=\psi (a_3)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,1)(3,3,0)$
TSO	Triply +1 Stable Ordinal	$\psi (\lambda \alpha .(\lambda \beta .(\lambda \gamma .\gamma +1-{\mathrm{\Pi }}_0)-{\mathrm{\Pi }}_0)-{\mathrm{\Pi }}_0=\psi (a_4)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,1)(3,3,1)(4,4,0)$
pfec LRO	pfec Large Rathjen Ordinal	$\psi (pfec.\omega -\pi -{\mathrm{\Pi }}_0)=\psi (a_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,2)$
SBO	Small Bashicu Ordinal	$\psi (pfec.\omega -\pi -{\mathrm{\Pi }}_0)=\psi (a_{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,2)$
pfec M2O	pfec min Σ2 Ordinal	$\psi (pfec.\min (a{\prec }_{{\mathrm{\Sigma }}_1}b{\prec }_{{\mathrm{\Sigma }}_2}c))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0)(1,1,1)(2,2,2)(3,2,2)(4,2,2)(4,2,1)$？
LRO	Large Rathjen Ordinal	$F\cap {\omega }_1^{\text{CK}},\theta =\omega$	$⩽\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)?$
TSSO / SSPO	Trio Sequence System Ordinal / Small Simple Projection Ordinal	$\psi (\omega -\text{proj.})=\psi (\sigma S\times \omega )=\psi (H^{\omega })$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)$
LSPO	Large Simple Projection Ordinal	$\psi (\min \alpha \text{ is }\alpha -\text{proj.})=\psi (\sigma S\times S)$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)(2,1,1,1)(3,1)(2)$
Q0.5BGO	QSS 0.5th Back Gear Ordinal	$\psi ({\psi }_S(\sigma S\times S\times \omega +S_2))$	$\mathrm{B}\mathrm{M}\mathrm{S}\mathrm{(}\mathrm{0}\mathrm{)}\mathrm{(}\mathrm{1},\mathrm{1},\mathrm{1},\mathrm{1}\mathrm{)}\mathrm{(}\mathrm{2},\mathrm{2}\mathrm{)}$
Q1BGO	QSS 1st Back Gear Ordinal	$\psi ({\psi }_S(\sigma S\times S\times \omega +S_{\omega }))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)(2,2,2)$
ESPO	Extend Simple Projection Ordinal	$\psi ({\psi }_S(\sigma S\times S\times {\omega }^2))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)(2,2,2,1)$
BOBO	Big Omega Back Ordinal	$\psi ((\omega ,0)-P)=\psi ({\psi }_H(H^{H\omega }))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1)(2,2,2,2)$
QSSO	Quardo Sequence System Ordinal	$\psi ({\psi }_H(H^{H^{\omega }}))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0,0,0,0,0)(1,1,1,1,1)$
TCAO	Trio Comprehension Axiom Ordinal	$\text{PTO}(({\mathrm{\Pi }}_3^1-CA{)}_0)$	$⩾\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1,1)$
QiSSO	Quinto Sequence System Ordinal	$\psi ({\psi }_H(H^{H^{H^{\omega }}}))$	$\mathrm{B}\mathrm{M}\mathrm{S}(0)(1,1,1,1,1,1)$
SHO / BMO	Small Hydra Ordinal / Bashicu Matrix Ordinal	$\psi ({\psi }_H({\epsilon }_{H+1}))?$	$Y(1,3)=\lim (\mathrm{B}\mathrm{M}\mathrm{S}\mathrm{)}$
βO	Beta Universe Ordinal	$\mathrm{P}\mathrm{T}\mathrm{O}\mathrm{(}{\mathrm{Z}}_{\mathrm{2}}\mathrm{)}$	$⩾Y(1,3)$
ΩSSO	Ω Sequence System Ordinal	$\psi ({\psi }_H(\phi (\mathrm{\Omega },H+1)))?$	$Y(1,3,4,2,5,8,10)$
LRPO	Large Right Projection Ordinal	$\psi ({\psi }_H(\phi (H,1)))?$	$Y(1,3,4,2,5,8,10,4,9,14,17,10)$
GHO	No-Go Hydra Ordinal	$\psi ({\psi }_H({\psi }_T(T_2\times 2)))?$	$Y(1,3,4,3)$
DCO	Difference Catching Ordinal	$\psi ({\psi }_H({\psi }_T(T_2\times {\psi }_T(T_2^2))))?$	$Y(1,3,5)$
SYO	Small Yukito Ordinal	$\omega \mathrm{M}\mathrm{N}\mathrm{(}\mathrm{0}\mathrm{)}\mathrm{(},,,\mathrm{1}\mathrm{)}$	$\lim (1-Y)=\omega -Y(1,4)$
MHO / ωYO	Medium Hydra Ordinal / ω-Y sequence Ordinal	$\omega \mathrm{2}\mathrm{M}\mathrm{N}\mathrm{(}\mathrm{0}\mathrm{)}\mathrm{(};\mathrm{1}\mathrm{)}$	$\lim (\omega -Y)$
CKO	Church-Kleene Ordinal	${\omega }_1^{\mathrm{C}\mathrm{K}}$
FUO	First Uncountable Ordinal	${\omega }_1$

已弃用序数表

缩写	英文全称	定义	大小	命名者
SMDO	Small Multidimensional Ordinal	${\omega }^{\omega }$	$(0)(1)(2)$	318`4
SHO	Small Hydra Ordinal	${\epsilon }_0=\psi (\mathrm{\Omega })$	$(0)(1,1)$	FataliS1024
ESVO	Extended Small Veblen Ordinal	$\psi \left({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\omega }}}\right)$	$(0)(1,1)(2,1)(3,1)(4,1)(5)$
ELVO	Extended Large Veblen Ordinal	$\psi \left({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}}}\right)$	$(0)(1,1)(2,1)(3,1)(4,1)(5,1)$
LDO(旧)	Large Dropping Ordinal	$\psi (\lambda \alpha .({\mathrm{\Omega }}_{\alpha \times 2})-{\mathrm{\Pi }}_0)$	$(0)(1,1,1)(2,2,1)(3,1)(2)$
EDO	Extended Dropping Ordinal	$\psi (\lambda \alpha .{\psi }_{I_{\alpha +1}}(I_{\alpha +1})-{\mathrm{\Pi }}_0)$	$(0)(1,1,1)(2,2,1)(3,2)$
SEIO	Small Eveog-Imagined Ordinal	${\mathrm{\Sigma }}_1\text{ adm.}$
MEIO	Medium Eveog-Imagined Ordinal	${\mathrm{\Sigma }}_2\text{ adm.}$
LEIO	Large Eveog-Imagined Ordinal	${\mathrm{\Sigma }}_3\text{ adm.}$
SOSO	Second Order Stable Ordinal	$\psi (1-o-{\mathrm{\Sigma }}_2-\text{stb.})$
EGO	Eveog's Ordinal	$\psi (\psi \sigma ({\sigma }_{\omega }))$	$(0)(1,1,1,1)(2,2,2,1)(3,2,1)(4)$
MHO	Medium Hydra Ordinal	$\lim (\mathrm{B}\mathrm{M}\mathrm{S})=\lim (0-Y)$	$Y(1,3)$	FataliS1024
LHO	Large Hydra Ordinal	$\lim (\omega -Y)$	$\mathrm{\Omega }-Y(1,3,12)$	FataliS1024
ZDO	Zeta Differenciating Ordinal	$\text{FOS911 }\mathrm{\Theta }({\zeta }_0)$	$\mathrm{\Omega }-Y(1,3,12)$
WYO	Omega Y Ordinal	$\lim (\mathrm{\Omega }-Y)$	$\mathrm{\Omega }-Y(1,\omega )$	318`4
EYO	Extended Y Ordinal	$\text{bFOS }\mathrm{\Theta }(\text{BHO})$	$\text{bFOS }(0)(1)(\omega )({\epsilon }_0)(\text{BHO})$	318`4
UCO	Upgrade Catching Ordinal	$\text{sFOS }\mathrm{\Theta }(\text{BHO})$	$\text{bFOS }\mathrm{\Theta }(\text{BO})$	318`4
XYO	Extreme Y Ordinal	$\text{bFOS }\mathrm{\Theta }(\text{BO})$	$\text{bFOS }(0)(1)(\omega )({\epsilon }_0)(\text{BO})$	318`4
DMO	Difference Matrix Ordinal	$\text{sFOS }\mathrm{\Theta }(\text{BO})$	$\text{bFOS }\mathrm{\Theta }(\text{SHO})$	318`4
GYO / 😰O	Grand Y-Sequence Ordinal / 😰 Ordinal	$\lim (X-Y)$	$\text{sFOS }(0)(1)(\omega )({\epsilon }_0)(\text{SHO})$	318`4
LDCO	Large Difference Catching Ordinal	$\text{sFOS }\mathrm{\Theta }(\text{SYO})$	$\text{b2-FOS }\mathrm{\Theta }({\zeta }_1)$	318`4
RHO	Remaining Hydra Ordinal	$\lim (\text{sFOS})$	$\text{b2-FOS }\mathrm{\Theta }(\phi (\omega ,0))$	318`4
WFO	Omega Fundamental Ordinal	$\lim (\text{Weak 2-FOS})$	$\text{b2-FOS }\mathrm{\Theta }({\mathrm{\Gamma }}_0)$	318`4
TMDO	Tri-Multidimensional Ordinal	$\text{s2-FOS }\mathrm{\Theta }(\phi (\omega ,0))$	$\omega 2-\text{RD}$	318`4
ERHO	Extended Remaining hydra Ordinal	$\lim (\text{b2-FOS})$	$\omega 2+1-\text{RD}$	318`4
LMDO	Large Multidimensional Ordinal	$\lim (\omega -\text{FOS})$	${\omega }^2-\text{RD}$	318`4
IFO	Infintesimal Function Ordinal	$\lim (\text{IFS})$	${\epsilon }_0-\text{RD}$	318`4
WRO	Omega Remaining Ordinal	$\lim (\text{ROS})$	$R\mathrm{\Omega }-Y$	318`4
SCLO	Small Code Lift Ordinal	$\sup (n-\text{code})$
EHO	Huge Hydra Ordinal	$\lim (\text{pfffz})$		夏夜星空
ROO	Remaining Omega Ordinal	$R_{\omega }\text{ remaining}$		318`4
UHO	Ultimate Hydra Ordinal	$\lim (\text{RSAM})$		夏夜星空
IHO	Infinite Hydra Ordinal	$\lim (\text{SAM})$		夏夜星空

本表取自 Worldly Sheet：

- （SCO/CO/LCO/HCO）谁起不重要，重要的是这是纪念康托尔的，如果没有他所有gggist今天(甚至永远)都走不到一起”

- 你们怎么把它弄成这样了，至少必要的（比如lim fffz/lim X-Y还是要的吧）

- fffz和X-Y公认理想之前搞这么多名字有什么用

- 不然MHO以上全都写成n-RD？- 不对 - 3184为什么要保留他造了那么多没用的序数缩写的黑历史？(bushi) - 不如还是加上 毕竟fatalis的SHO/MHO/LHO都有了

DNAO

DNAO（Disgusting Nonsense Annoyance Ordinal）

定义：

(0)(1,1,1)(2,2,2)(3,3,3)(3,3,0)(4,4,1)(5,5,2)(6,6,2)(7,7,0)(8,8,1)(9,9,2)(10,9,2)(11,9,0)(12,10,1)(13,11,2)(13,11,2)(13,11,1)(14,12,2)(14,11,1)(15,12,2)(15,11,1)(16,12,0)(17,13,1)(18,14,2)(18,14,2)(18,14,1)(19,15,2)(19,14,1)(20,15,2)(20,14,1)(21,15,0)(22,16,1)(23,17,2)(23,17,2)(23,17,1)(24,18,2)(24,17,1)(25,18,2)(25,17,0)(26,18,1)(27,19,2)(27,19,2)(27,19,1)(28,20,2)(28,19,1)(29,20,2)(29,19,0)(30,20,1)(31,21,2)(31,21,2)(31,21,1)(32,22,2)(32,21,1)(33,22,2)(33,21,0)(34,22,1)(35,23,2)(35,23,2)(35,23,1)(36,24,2)(36,23,1)(37,24,2)(37,23,0)(38,24,1)(39,25,2)(40,25,2)(40,25,1)(41,26,2)(41,22,1)(42,23,2)(42,23,2)(42,23,1)(43,24,2)(43,23,1)(44,24,2)(44,23,0)(45,24,1)(46,25,2)(47,25,2)(47,25,1)(48,26,1)(49,27,0)(50,28,1)(51,29,2)(52,29,2)(52,29,1)(53,30,0)(54,31,1)(55,32,2)(56,32,2)(56,32,0)(57,33,1)(58,34,2)(59,34,2)(59,34,0)(60,35,1)(61,36,2)(62,36,2)(62,36,0)(63,37,1)(64,38,2)(65,38,2)(65,38,0)(66,39,1)(67,40,2)(68,40,2)(68,40,0)(69,41,1)(70,42,2)(71,42,2)(71,42,0)(72,43,1)(73,44,0)(74,45,1)(75,44,0)(76,45,1)(77,46,0)(78,47,0)(79,44,0)(80,45,1)(81,46,0)(82,47,0)(83,44,0)(84,45,1)(85,46,0)(86,47,0)(87,44,0)(88,45,1)(89,46,0)(90,47,0)(91,44,0)(92,45,1)(93,46,0)(94,47,0)(95,44,0)(96,45,1)(96,45,1)(96,45,1)(96,45,0)(97,46,0)(98,47,0)(99,48,0)(100,47,0)(101,48,0)(102,47,0)(103,48,0)(104,47,0)(105,48,0)(106,47,0)(107,48,0)(108,45,0)(109,46,0)(110,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,46,0)(112,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,46,0)(114,47,0)(115,46,0)(116,47,0)(117,46,0)(118,47,0)(119,46,0)(120,45,0)(121,46,0)(122,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,46,0)(124,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,46,0)(126,47,0)(127,46,0)(128,47,0)(129,46,0)(130,47,0)(131,46,0)(132,45,0)(133,46,0)(134,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,46,0)(136,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,46,0)(138,47,0)(139,46,0)(140,47,0)(141,46,0)(142,47,0)(143,46,0)(144,45,0)(145,46,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(149,45,0)(149,45,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(152,45,0)(152,45,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(150,45,0)(149,45,0)