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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 === {| class="wikitable" |- ! 缩写 !! 英文全称 !! 常规表示方法([[序数坍缩函数#BOCF|BOCF]] 等) !! [[BMS]] / [[Y序列|Y]] |- | [[FTO]]|| First Transfinite Ordinal || <math>\omega</math>|| <math>\mathrm{BMS}(0)(1)</math> |- | [[LAO]]|| Linear Array Ordinal<ref>因为在googology一度经典的线性数阵的极限是它,因此得名</ref>|| <math>\omega^\omega</math>|| <math>\mathrm{BMS}(0)(1)(2)</math> |- | [[SCO]]|| Small Cantor Ordinal || <math>\varphi(1,0)=\varepsilon_0=\psi(\Omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)</math> |- | [[CO]]|| Cantor Ordinal || <math>\varphi(2,0)=\zeta_0=\psi(\Omega^2)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)</math> |- |[[LCO]] |Large Cantor Ordinal |<math>\varphi(3,0)=\eta_0=\psi(\Omega^3)</math> |<math>\mathrm{BMS}(0,0)(1,1)(2,1)(2,1)</math> |- | [[HCO]]|| Hyper Cantor Ordinal || <math>\varphi(\omega,0)=\psi(\Omega^\omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,0)</math> |- | [[FSO]]|| Feferman-Schütte Ordinal || <math>\varphi(1,0,0)=\Gamma_0=\psi(\Omega^\Omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)</math> |- |[[ACO]] |Ackermann Ordinal |<math>\varphi(1,0,0,0)=\psi(\Omega^{\Omega^2})</math> |<math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(3,1)</math> |- | [[SVO]]|| Small Veblen Ordinal || <math>\psi(\Omega^{\Omega^\omega})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(4,0)</math> |- | [[LVO]]|| Large Veblen Ordinal || <math>\psi(\Omega^{\Omega^\Omega})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(4,1)</math> |- | [[BHO]]|| Bachmann-Howard Ordinal || <math>\psi(\Omega_{2})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,2)</math> |- | [[BO]]|| Buchholz's Ordinal || <math>\psi(\Omega_{\omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)</math> |- | [[TFBO]]|| Takeuti-Feferman-Buchholz Ordinal || <math>\psi(\Omega_{\omega+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,0)(3,2,0)</math> |- | [[BIO]]|| Bird's Ordinal<ref>鸟之数阵第四版的极限是它,因此得名</ref>|| <math>\psi(\Omega_{\Omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)</math> |- | [[EBO]]|| Extended Buchholz Ordinal || <math>\psi(I)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)</math> |- | [[JO]]|| Jager's Ordinal || <math>\psi(\Omega_{I+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)</math> |- | [[SIO]]|| Small Inaccessible Ordinal || <math>\psi(I_{\omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)</math> |- | [[MBO]]|| Mutiply Buchholz Ordinal || <math>\psi(I(\omega,0))=\psi(M^\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)</math> |- |[[TBO]] |Transfinitary Buchholz's Ordinal |<math>\psi(I(1,0,0))=\psi(M^M)</math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)</math> |- | [[SRO]]|| Small Rathjen Ordinal || <math>\psi(\varepsilon_{M+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)</math> |- | [[SMO]]|| Small Mahlo Ordinal || <math>\psi(M_\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)</math> |- |[[SNO]] |Small 1-Mahlo (N) Ordinal |<math>\psi(N_\omega)</math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)</math> |- | [[RO]]|| Rathjen's Ordinal || <math>\psi(\varepsilon_{K+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0)</math> |- |[[SKO]] |Small Weakly Compact (K) Ordinal |<math>\psi(K_\omega)</math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)</math> |- |[[DO]] |Duchhart's Ordinal |<math>\psi(2 \ \rm{aft} \ 4)</math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,0)(6,2,0)</math> |- | [[SSO]]|| Small Stegert Ordinal || <math>\psi(psd.\Pi_{\omega})=\psi(a_2)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)</math> |- | [[LSO]]|| Large Stegert Ordinal || <math>\psi(\lambda\alpha.(\alpha\times 2)-\Pi_{0})=\psi(a_2^a)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,0)(2,0,0)</math> |- |[[APO]] |Admissible-parameter free effective cardinal Ordinal |<math>\psi(\lambda\alpha.(\Omega_{\alpha+1})-\Pi_1)=\psi(a_2^{\Omega_{a+1}}+\psi_{a_2}(a_2^{\Omega_{a+1}})\times\omega)</math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,1)</math> |- | [[BGO]]|| TSS 1st Back Gear Ordinal (CN ggg)<ref>Bashicu对BGO的原定义是BMS(0,0,0)(1,1,1)(2,2,0)。BGO指(0,0,0)(1,1,1)(2,2,1)是中文googology社区的重命名</ref>|| <math>\psi(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_{1})=\psi(\Omega_{a_2+1}+\psi_{a_2}(\Omega_{a_2+1})\times\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)</math> |- | [[SDO]]|| Small Dropping Ordinal || <math>\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_{0}=\psi(\Omega_{a_2+1}\times\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,0,0)</math> |- | [[LDO]]|| Large Dropping Ordinal || <math>\psi(\lambda\alpha.(\psi_{I_{\alpha+1}}(0))-\Pi_{0})=\psi(\Omega_{a_2+1}\times a_2)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> |- |[[DSO]] |Doubly +1 Stable Ordinal |<math>\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_0)-\Pi_0=\psi(a_3) </math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,3,0)</math> |- |[[TSO]] |Triply +1 Stable Ordinal |<math>\psi(\lambda\alpha.(\lambda\beta.(\lambda\gamma.\gamma+1-\Pi_0)-\Pi_0)-\Pi_0=\psi(a_4) </math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,3,1)(4,4,0)</math> |- | [[LRO|pfec LRO]]|| pfec Large Rathjen Ordinal || <math>\psi(pfec.\omega-\pi-\Pi_{0})=\psi(a_\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)</math> |- |[[LRO|SBO]] |Small Bashicu Ordinal | <math>\psi(pfec.\omega-\pi-\Pi_{0})=\psi(a_\omega) </math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)</math> |- |[[方括号稳定|pfec M2O]] |pfec min Σ<sub>2</sub> Ordinal |<math>\psi(pfec.\min(a\prec_{\Sigma_1}b\prec_{\Sigma_2}c)) </math> |<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)(3,2,2)(4,2,2)(4,2,1)</math>? |- |[[LRO]] |Large Rathjen Ordinal |<math>F\cap\omega_1^\text{CK},\theta=\omega </math> |<math>\leqslant\mathrm{BMS}(0)(1,1,1,1)?</math> |- |[[TSSO]] / SSPO |Trio Sequence System Ordinal / Small Simple Projection Ordinal |<math>\psi(\omega-\text{proj.})=\psi(\sigma S\times \omega)=\psi(H^\omega)</math> |<math>\mathrm{BMS}(0)(1,1,1,1)</math> |- |[[LSPO]] |Large Simple Projection Ordinal |<math>\psi(\min\ \alpha\text{ is }\alpha-\text{proj.})=\psi(\sigma S\times S) </math> |<math>\mathrm{BMS}(0)(1,1,1,1)(2,1,1,1)(3,1)(2)</math> |- |[[Q0.5BGO]] |QSS 0.5th Back Gear Ordinal |<math>\psi(\psi_S(\sigma S\times S\times \omega+S_2)) </math> |<math>\rm{BMS}(0)(1,1,1,1)(2,2)</math> |- |[[Q1BGO]] |QSS 1st Back Gear Ordinal | <math>\psi(\psi_S(\sigma S\times S\times \omega+S_\omega)) </math> |<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2)</math> |- |[[ESPO]] |Extend Simple Projection Ordinal | <math>\psi(\psi_S(\sigma S\times S\times \omega^2)) </math> |<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2,1)</math> |- |[[BOBO]] |Big Omega Back Ordinal | <math>\psi((\omega,0)-P)=\psi(\psi_{H}(H^{H\omega})) </math> |<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2,2)</math> |- | [[QSSO]]|| Quardo Sequence System Ordinal || <math>\psi(\psi_{H}(H^{H^{\omega}}))</math>|| <math>\mathrm{BMS}(0,0,0,0,0)(1,1,1,1,1)</math> |- |[[QSSO|TCAO]] |Trio Comprehension Axiom Ordinal |<math>\text{PTO}((\Pi_3^1-CA)_0) </math> |<math>\geqslant\mathrm{BMS}(0)(1,1,1,1,1)</math> |- |QiSSO |Quinto Sequence System Ordinal | <math>\psi(\psi_{H}(H^{H^{H^{\omega}}}))</math> |<math>\mathrm{BMS}(0)(1,1,1,1,1,1)</math> |- | [[SHO]] / BMO<ref name=":0">SHO,MHO的名字均来自FataliS1024.但原定义的SHO指的是<math>\varepsilon_0</math>,MHO指的是BMS极限。还有一个LHO指<math>\omega -Y</math>极限。但后来不知为何变成了现在的这个版本,而LHO成为了无定义的名字</ref>|| Small Hydra Ordinal / Bashicu Matrix Ordinal || <math>\psi(\psi_{H}(\varepsilon_{H+1}))?</math>|| <math>Y(1,3)=\lim(\rm BMS)</math> |- |βO |Beta Universe Ordinal |<math>\rm PTO(Z_2)</math> |<math>\geqslant Y(1,3)</math> |- | [[ΩSSO]]|| Ω Sequence System Ordinal || <math>\psi(\psi_H(\varphi(\Omega,H+1)))?</math>|| <math>Y(1,3,4,2,5,8,10)</math> |- |[[LRPO]] |Large Right Projection Ordinal |<math>\psi(\psi_{H}(\varphi(H,1)))?</math> |<math>Y(1,3,4,2,5,8,10,4,9,14,17,10)</math> |- | [[GHO]]|| No-Go Hydra Ordinal<ref>原名Guo bu qu de Hydra Ordinal,但过于口语化和非正式。而这个序数本身确实是一个重要的序数。曹知秋将名字改成了现在的版本</ref>|| <math>\psi(\psi_H(\psi_T(T_2\times 2)))?</math>|| <math>Y(1,3,4,3)</math> |- |[[DCO]] |Difference Catching Ordinal |<math>\psi(\psi_H(\psi_T(T_2\times\psi_T(T_2^2))))?</math> |<math>Y(1,3,5)</math> |- | [[SYO]]|| Small Yukito Ordinal || <math>\omega \rm{ MN}(0)(,,,1)</math>|| <math>\lim(1-Y)=\omega-Y(1,4)</math> |- | [[MHO]] / ωYO<ref name=":0" />|| Medium Hydra Ordinal / ω-Y sequence Ordinal || <math>\omega \rm{2MN}(0)(;1)</math>|| <math>\lim(\omega-Y)</math> |- | [[CKO]]|| Church-Kleene Ordinal || <math>\omega_{1}^{\rm CK}</math> |- | [[FUO]]|| First Uncountable Ordinal || <math>\omega_{1}</math>|| |} === 已弃用序数表 === {| class="wikitable" !缩写 !英文全称 !定义 !大小 !命名者 |- |SMDO |Small Multidimensional Ordinal |<math>\omega^\omega</math> |<math>(0)(1)(2)</math> |318`4 |- |SHO |Small Hydra Ordinal |<math>\varepsilon_0=\psi(\Omega)</math> |<math>(0)(1,1)</math> |FataliS1024 |- |ESVO |Extended Small Veblen Ordinal |<math>\psi\left(\Omega^{\Omega^{\Omega^{\omega}}}\right)</math> |<math>(0)(1,1)(2,1)(3,1)(4,1)(5)</math> | |- |ELVO |Extended Large Veblen Ordinal |<math>\psi\left(\Omega^{\Omega^{\Omega^{\Omega}}}\right)</math> |<math>(0)(1,1)(2,1)(3,1)(4,1)(5,1)</math> | |- |LDO(旧) |Large Dropping Ordinal |<math>\psi(\lambda\alpha.(\Omega_{\alpha\times 2})-\Pi_{0})</math> |<math>(0)(1,1,1)(2,2,1)(3,1)(2)</math> | |- |EDO |Extended Dropping Ordinal |<math>\psi(\lambda\alpha.\psi_{I_{\alpha+1}}(I_{\alpha+1})-\Pi_0)</math> |<math>(0)(1,1,1)(2,2,1)(3,2)</math> | |- |SEIO |Small Eveog-Imagined Ordinal |<math>\Sigma_1\text{ adm.}</math> | | |- |MEIO |Medium Eveog-Imagined Ordinal |<math>\Sigma_2\text{ adm.}</math> | | |- |LEIO |Large Eveog-Imagined Ordinal |<math>\Sigma_3\text{ adm.}</math> | | |- |SOSO |Second Order Stable Ordinal |<math>\psi(1-o-\Sigma_2-\text{stb.})</math> | | |- |EGO |Eveog's Ordinal |<math>\psi(\psi\sigma(\sigma_\omega))</math> |<math>(0)(1,1,1,1)(2,2,2,1)(3,2,1)(4)</math> | |- |MHO |Medium Hydra Ordinal |<math>\lim({\rm BMS})=\lim(0-Y)</math> |<math>Y(1,3)</math> |FataliS1024 |- |LHO |Large Hydra Ordinal |<math>\lim(\omega-Y)</math> |<math>\Omega-Y(1,3,12)</math> |FataliS1024 |- |ZDO |Zeta Differenciating Ordinal |<math>\text{FOS911 }\Theta(\zeta_0)</math> |<math>\Omega-Y(1,3,12)</math> | |- |WYO |Omega Y Ordinal |<math>\lim(\Omega-Y)</math> |<math>\Omega-Y(1,\omega)</math> |318`4 |- |EYO |Extended Y Ordinal |<math>\text{bFOS }\Theta(\text{BHO})</math> |<math>\text{bFOS }(0)(1)(\omega)(\varepsilon_0)(\text{BHO})</math> |318`4 |- |UCO |Upgrade Catching Ordinal |<math>\text{sFOS }\Theta(\text{BHO})</math> |<math>\text{bFOS }\Theta(\text{BO})</math> |318`4 |- |XYO |Extreme Y Ordinal |<math>\text{bFOS }\Theta(\text{BO})</math> |<math>\text{bFOS }(0)(1)(\omega)(\varepsilon_0)(\text{BO})</math> |318`4 |- |DMO |Difference Matrix Ordinal |<math>\text{sFOS }\Theta(\text{BO})</math> |<math>\text{bFOS }\Theta(\text{SHO})</math> |318`4 |- |GYO / 😰O |Grand Y-Sequence Ordinal / 😰 Ordinal |<math>\lim(X-Y)</math> |<math>\text{sFOS }(0)(1)(\omega)(\varepsilon_0)(\text{SHO})</math> |318`4 |- |LDCO |Large Difference Catching Ordinal |<math>\text{sFOS }\Theta(\text{SYO})</math> |<math>\text{b2-FOS }\Theta(\zeta_1)</math> |318`4 |- |RHO |Remaining Hydra Ordinal |<math>\lim(\text{sFOS})</math> |<math>\text{b2-FOS }\Theta(\varphi(\omega,0))</math> |318`4 |- |WFO |Omega Fundamental Ordinal |<math>\lim(\text{Weak 2-FOS})</math> |<math>\text{b2-FOS }\Theta(\Gamma_0)</math> |318`4 |- |TMDO |Tri-Multidimensional Ordinal |<math>\text{s2-FOS }\Theta(\varphi(\omega,0))</math> |<math>\omega2-\text{RD}</math> |318`4 |- |ERHO |Extended Remaining hydra Ordinal |<math>\lim(\text{b2-FOS})</math> |<math>\omega2+1-\text{RD}</math> |318`4 |- |LMDO |Large Multidimensional Ordinal |<math>\lim(\omega-\text{FOS})</math> |<math>\omega^2-\text{RD}</math> |318`4 |- |IFO |Infintesimal Function Ordinal |<math>\lim(\text{IFS})</math> |<math>\varepsilon_0-\text{RD}</math> |318`4 |- |WRO |Omega Remaining Ordinal |<math>\lim(\text{ROS})</math> |<math>R\ \Omega-Y</math> |318`4 |- |SCLO |Small Code Lift Ordinal |<math>\sup(n-\text{code})</math> | | |- |EHO |Huge Hydra Ordinal |<math>\lim(\text{pfffz})</math> | |夏夜星空 |- |ROO |Remaining Omega Ordinal |<math>R_\omega\text{ remaining}</math> | |318`4 |- |UHO |Ultimate Hydra Ordinal |<math>\lim(\text{RSAM})</math> | |夏夜星空 |- |IHO |Infinite Hydra Ordinal |<math>\lim(\text{SAM})</math> | |夏夜星空 |} 本表取自 [https://docs.qq.com/sheet/DSnFWckliSU5TTE15 Worldly Sheet]:<blockquote>- (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</blockquote> ==== 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) 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