CoCalc Public FilesPSET10-f.ipynb
Author: Daishi Kiyohara
Views : 86
Description: Sage worksheet for problemset 10 problem 2
Compute Environment: Ubuntu 20.04 (Default)
In [1]:
A9=AlternatingGroup(9)
for a in A9:
for b in A9:
if A9.subgroup([a,b]) == A9 and a**3==a and b**4==b:
print (a,b)
break

--------------------------------------------------------------------------- KeyboardInterrupt Traceback (most recent call last) <ipython-input-1-64887185b270> in <module> 2 for a in A9: 3 for b in A9: ----> 4 if A9.subgroup([a,b]) == A9 and a**Integer(3)==a and b**Integer(4)==b: 5 print (a,b) 6 break src/cysignals/signals.pyx in cysignals.signals.python_check_interrupt() KeyboardInterrupt: 
In [4]:
A9=AlternatingGroup(9)
for a,b in ((a_1,b_1) for a_1 in A9 for b_1 in A9):
if a.ord()==2 and b.ord()==3:
if A9.subgroup([a,b]) == A9:
print (a,b)
break

--------------------------------------------------------------------------- AttributeError Traceback (most recent call last) <ipython-input-4-a1008408c3e3> in <module> 1 A9=AlternatingGroup(Integer(9)) 2 for a,b in ((a_1,b_1) for a_1 in A9 for b_1 in A9): ----> 3 if a.ord()==Integer(2) and b.ord()==Integer(3): 4 if A9.subgroup([a,b]) == A9: 5 print (a,b) /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4703)() 491 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' 492 """ --> 493 return self.getattr_from_category(name) 494 495 cdef getattr_from_category(self, name): /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4815)() 504 else: 505 cls = P._abstract_element_class --> 506 return getattr_from_other_class(self, cls, name) 507 508 def __dir__(self): /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/cpython/getattr.pyx in sage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2620)() 370 dummy_error_message.cls = type(self) 371 dummy_error_message.name = name --> 372 raise AttributeError(dummy_error_message) 373 attribute = <object>attr 374 # Check for a descriptor (__get__ in Python) AttributeError: 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement' object has no attribute 'ord' 
In [7]:
A9=AlternatingGroup(9)
for a in A9:
if a.order()==2:
for b in A9:
if b.order()==3:
if A9.subgroup([a,b]) == A9:
print (a,b)
break

(1,3)(2,7)(4,8)(5,9) (1,2,7)(3,8,5)(4,9,6) (1,9)(2,3)(5,7)(6,8) (1,5,3)(2,8,6)(4,9,7) (1,6)(2,7)(4,8)(5,9) (1,2,7)(3,8,5)(4,9,6) (1,3)(2,5)(4,8)(6,7) (1,2,9)(3,5,4)(6,7,8) (1,9)(2,3)(4,5)(6,8) (1,6,2)(3,5,4)(7,9,8) (1,7)(2,6)(3,4)(5,8) (1,7,6)(2,8,4)(3,9,5) (1,3)(2,8)(4,7)(6,9) (1,2,7)(3,8,5)(4,9,6) (1,6)(2,7)(3,9)(5,8) (1,9,5)(2,7,6)(3,8,4) (1,9)(2,4)(3,7)(6,8) (1,3,5)(2,9,7)(4,8,6) (1,6)(2,8)(3,4)(7,9) (1,3,5)(2,9,7)(4,8,6) (1,3)(2,5)(4,9)(6,7) (1,6,5)(2,8,7)(3,4,9) (1,3)(2,9)(4,6)(7,8) (1,6,5)(2,8,7)(3,4,9) (1,7)(2,6)(3,9)(5,8) (1,9,5)(2,7,6)(3,8,4) (1,3)(2,4)(6,7)(8,9) (1,9,5)(2,7,6)(3,8,4) (2,7)(3,6)(4,9)(5,8) (1,5,3)(2,8,6)(4,9,7) (1,3)(4,5)(6,7)(8,9) (1,3,5)(2,9,7)(4,8,6) (1,3)(2,5)(6,7)(8,9) (1,9,5)(2,7,6)(3,8,4) (1,3)(2,6)(4,8)(5,9) (1,6,2)(3,5,4)(7,9,8) (1,4)(2,7)(5,8)(6,9) (1,9,5)(2,7,6)(3,8,4)
--------------------------------------------------------------------------- KeyboardInterrupt Traceback (most recent call last) <ipython-input-7-1da3029ad08b> in <module> 4 for b in A9: 5 if b.order()==Integer(3): ----> 6 if A9.subgroup([a,b]) == A9: 7 print (a,b) 8 break /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/structure/richcmp.pyx in sage.structure.richcmp.slot_tp_richcompare (build/cythonized/sage/structure/richcmp.c:1878)() 271 Function to put in the tp_richcompare slot. 272 """ --> 273 return self.__richcmp__(other, op) 274 275 /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/groups/perm_gps/permgroup.py in __richcmp__(self, other, op) 4864 return NotImplemented 4865 -> 4866 c = PermutationGroup_generic.__richcmp__(self, other, op_EQ) 4867 if not c: 4868 return PermutationGroup_generic.__richcmp__(self, other, op) /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/groups/perm_gps/permgroup.py in __richcmp__(self, right, op) 713 gRight = right._libgap_() 714 if op in [op_EQ,op_NE]: --> 715 return gSelf._richcmp_(gRight, op) 716 717 if gSelf.IsSubgroup(gRight): /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/libs/gap/element.pyx in sage.libs.gap.element.GapElement._richcmp_ (build/cythonized/sage/libs/gap/element.c:9658)() 861 return hash(str(self)) 862 --> 863 cpdef _richcmp_(self, other, int op): 864 """ 865 Compare self with other. /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/libs/gap/element.pyx in sage.libs.gap.element.GapElement._richcmp_ (build/cythonized/sage/libs/gap/element.c:9404)() 929 return self._compare_equal(other) or self._compare_less(other) 930 elif op == Py_EQ: --> 931 return self._compare_equal(other) 932 elif op == Py_GT: 933 return not self._compare_less(other) and not self._compare_equal(other) /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/libs/gap/element.pyx in sage.libs.gap.element.GapElement._compare_equal (build/cythonized/sage/libs/gap/element.c:9762)() 953 return id(self) == id(other) 954 cdef GapElement c_other = <GapElement>other --> 955 sig_on() 956 try: 957 GAP_Enter() KeyboardInterrupt: 
In [11]:
A9=AlternatingGroup(9)
for a in A9:
if a.order()==2:
for b in A9:
if b.order()==3:
if A9.subgroup([a,b]) == A9:
H=A9.subgroup([a,b]).as_finitely_presented_group().simplified()
G=SL(2,Integers()); S=G([0,-1,1,0]); T=G([1,1,0,1])
for i in range(2,len(H.relations())):
print(H.relations()[i].subs(a=S,b=S*T),"\n")
break

[-1 0] [14 -1] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [-1 0] [24 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [-1 0] [30 -1] [-1 0] [38 -1] [ 1 0] [-38 1] [ 1 0] [-39 1] [ -1 -45] [ 0 -1] [ 1 48] [ 0 1] [ 1 51] [ 0 1] [-1 0] [15 -1] [ 1 24] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-29 1] [ 1 0] [-33 1] [ -1 -38] [ 0 -1] [-1 0] [44 -1] [-1 0] [46 -1] [-1 0] [50 -1] [ 1 0] [-50 1] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [-1 0] [30 -1] [-1 0] [31 -1] [ 1 31] [ 0 1] [ 1 0] [-32 1] [-1 0] [38 -1] [-1 0] [38 -1] [-1 0] [38 -1] [-1 0] [40 -1] [ 1 0] [-48 1] [ 1 51] [ 0 1] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-30 1] [ 1 0] [-30 1] [-1 0] [30 -1] [-1 0] [32 -1] [-1 0] [36 -1] [-1 0] [45 -1] [-1 0] [51 -1] [-1 0] [53 -1] [ 1 61] [ 0 1] [ 1 0] [-63 1] [-1 0] [63 -1] [-1 0] [96 -1] [ 1 0] [-15 1] [ 1 24] [ 0 1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ -1 -33] [ 0 -1] [ 1 0] [-35 1] [ -1 -36] [ 0 -1] [ 1 0] [-36 1] [-1 0] [39 -1] [ 1 46] [ 0 1] [ 1 0] [-48 1] [ 1 0] [15 1] [119508 53911] [ 50141 22619] [33588241 52102575] [56733915 88006486] [ 203471149 695803884] [ 531767916 1818470005] [ 384482134414 -169740266973] [-526511993957 232443274783] [-2738038845544 -1979646147183] [-2117508679473 -1530992851240] [10475987429429 17081945151359] [ 6202346160768 10113427267997] [191508235080089 521480005881363] [103387733264841 281526461399756] [ -569503398719896 -774961458460025] [ -928621371317687 -1263637361763056] [2096134342728547 868186982525820] [5056579650401663 2094358428796663] [-1615710887487374 -2598182141384301] [-2182163819651099 -3509080188603200] [281693410859735135 110403563141103494] [ 48804514404865261 19127860574457681] [ -754798588957958723 1061914081847140296] [ 985968808998884249 -1387143772994368835] [ 52273914397704629905 -40344481833764353854] [-11105586115180638496 8571179764125047857] [-124814744742810687423 -44352648775647958603] [ -45029043466232924558 -16000972911305420325] [59938792538616692458489 12560855077498245992023] [42377822790323601775859 8880754316600751374022] [-165515424969580647400611 -564807914517549949133225] [ -67640303791659044664628 -230817030672046282362791] [ 1197149893509438656269899 -1693224433232363401544344] [-5712645747347144614902956 8079849825198916970205635] [-18373445864139486777476362 -26127899446870546982615703] [-31365913862847754707687583 -44603796670890358796051425] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 24] [ 0 1] [ 1 24] [ 0 1] [ 1 28] [ 0 1] [-1 0] [30 -1] [-1 0] [31 -1] [ 1 0] [-31 1] [-1 0] [39 -1] [ 1 42] [ 0 1] [ -1 -43] [ 0 -1] [ 1 0] [-59 1] [119508 53911] [ 50141 22619] [ -28652104 -7763365] [-101781395 -27577944] [-768210187 -450031145] [-285474407 -167235968] [ -498939946 -689239207] [-1906884863 -2634184377] [-1377455834 -1962518153] [-3120103093 -4445339595] [-18753416456 -11405800987] [-14831696205 -9020616356] [-14975211813 -4390281500] [-50618446399 -14839805377] [70760351569 13083129945] [86963016925 16078897654] [377888654221 600623181828] [208263657964 331018090933] [519689014502 179035774557] [217599477937 74964238205] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [ -3274648482745 -12335803273277] [ -618342945117 -2329336100218] [142859544220579 42233773454388] [102626213146903 30339535661935] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [1891855886353448405 2607196171611135953] [4285281269703483273 5905613107868883314] [-1 0] [14 -1] [ 1 0] [-15 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-30 1] [-1 0] [32 -1] [ 1 0] [-34 1] [ -1 -36] [ 0 -1] [-1 0] [36 -1] [ 1 0] [-39 1] [ -1 -40] [ 0 -1] [ 1 0] [-40 1] [ 1 0] [-40 1] [ 1 0] [-15 1] [ 1 0] [-20 1] [ 1 0] [-26 1] [ 1 0] [-26 1] [-1 0] [26 -1] [ 1 32] [ 0 1] [ 1 0] [-32 1] [ 1 0] [-32 1] [ 1 0] [-33 1] [-1 0] [34 -1] [ 1 0] [-38 1] [ 1 0] [-40 1] [ 1 0] [-43 1] [-1 0] [46 -1] [-1 0] [51 -1] [ 1 0] [-58 1] [19371 10855] [15197 8516] [ 43601 -27040] [-113906 70641] [65597 53911] [93119 76530] [ 33487 -20748] [-159796 99007] [9189282 3265355] [3587449 1274778] [ 5855101 15959302] [ 2388424 6510149] [ 10107648 -36146407] [-12281897 43921835] [ -51930939 -14231263] [-167459087 -45890838] [1557482521 854361489] [ 572472813 314031598] [3529309795 4802600656] [5708333304 7767763915] [1191757004 5528798881] [ 729859291 3385963093] [ 2778933387 12893377174] [ 1717221305 7967366933] [-33445150586 7194006981] [ 54621164115 -11748939056] [110757848459 625647878790] [ 87503394214 494288339279] [-8662563485365 -5356528757966] [-5482208485179 -3389944265071] [3089591080357 5011240158039] [ 855227863150 1387158397543] [ -95754682995 247091743499] [ 456820700086 -1178810474017] [ -8682155347241 -4864221782993] [-11996684188505 -6721203459226] [203120133635988247057 77165499085523664367] [740284709777553686418 281234745531133427551] [ 1 0] [15 1] [1103 1426] [ 782 1011] [3070 5229] [2241 3817] [25359 92059] [14006 50845] [ 51874 22443] [141347 61153] [-110878 -46637] [ -87643 -36864] [ 48589 132618] [ 10295 28099] [1213808 947103] [3907633 3049025] [ 9178274 15038517] [23683413 38805053] [-7414755 -4553518] [-6432818 -3950495] [ 244441 1028280] [ 135300 569161] [ 17957829 31089715] [ 61968995 107284594] [40163759 47363680] [10883600 12834639] [122722897 54260455] [100875030 44600683] [ 23974252 114400247] [ 37867401 180695524] [ 651012663 1131433238] [ 277194208 481752135] [ 96511 155701] [ 28275 45616] [ 107337 -73513] [-140261 96062] [ 5031733 1292264] [17874317 4590533] [212350319 80723124] [172230444 65471903] [ 234334241 413619382] [ 603531592 1065283345] [-18753416456 -11405800987] [-14831696205 -9020616356] [-350777034 -91395275] [-985646491 -256811089] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [120334732494509 205628578706521] [ 73187518576039 125063189254480] [ -330220265171428 -758431267745689] [ -523900826521663 -1203265849918586] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [ -870348302415853 2970826136481609] [ 3787814482207630 -12929235609066907] [ 8300294033183311 -3498613131310525] [-18548910168645691 7818453229256816] [ 84395688772766589 49964955551705081] [204248046901642006 120921396973730483] [ 60993630059966673849 21012646979452286051] [259847650563036404878 89518970167097861571] [ 1 0] [15 1] [ 2901 2000] [10300 7101] [ 43601 -27040] [-113906 70641] [119508 50141] [ 53911 22619] [-180135 -109564] [-142286 -86543] [295401 538265] [180883 329596] [1936616 3336435] [1141477 1966556] [ 834641 1025280] [1409760 1731761] [ 692206 -423943] [-1503605 920886] [-3450378 2439269] [ 523657 -370203] [42892881 30195610] [12668480 8918321] [ -3470585 8228778] [ 7750173 -18375707] [ 96162613 62461702] [228064322 148137465] [-2880208785 -1987984552] [-1754773607 -1211184009] [ -7762839698 -10979742383] [-21899128469 -30974076286] [ 135458817123 -75589784243] [-240223264567 134051257234] [-566368739356397 -215115230901461] [-234697229154146 -89141481747031] [2262784717636705 1459092625340131] [ 662953270246169 427486636276908] [ 1 0] [15 1] [65597 53911] [93119 76530] [ 57511 207844] [ 20748 74983] [ -7936617 -11491202] [-12836533 -18585651] [-43066064 -11650005] [-27763955 -7510559] [ 2707133 -9238170] [-11788142 40227377] [ -28652104 -7763365] [-101781395 -27577944] [-65351109870 -39746451257] [-51871740427 -31548318102] [ 74928070698 21966449951] [253267910821 74249835014] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ -86052924347 490208032251] [ 289257798264 -1647782421995] [-162158031001517 -88959075420045] [-114744880904774 -62948461148843] [122488901181931 46528259362732] [344979108895876 131042709164243] [ 4197406814380097 -1623242560393632] [-5174532694362354 2001121661798657] [2763142942423999 3351472833487422] [4470606858841155 5422490891283589] [119508 53911] [ 50141 22619] [ 95731 -20748] [-169624 36763] [ 8393958 12153373] [13576397 19656879] [ -28652104 -7763365] [-101781395 -27577944] [-1240964909 -1006513016] [-2865754614 -2324335925] [-18753416456 -11405800987] [-14831696205 -9020616356] [-14975211813 -4390281500] [-50618446399 -14839805377] [ -27783489050 -106184767181] [ -11459125629 -43795240577] [377888654221 600623181828] [208263657964 331018090933] [ 50284633493 116479845582] [ 21842221103 50595547079] [ -15887048212 54221102113] [ 69141504763 -235973891435] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [207253887903 878850653723] [127202447773 539396174960] [5959573337456 2274927811835] [7352453112445 2806627106271] [ -333631872868991 -1256811804235783] [ -62998796894495 -237320346251046] [ 16933581617178329 -10466120360526030] [-11796885764338215 7291288345265819] [-233 -377] [-377 -610] [ -1 -15] [ 0 -1] [1576 2241] [3735 5311] [78077 50024] [56446 36165] [ 32649 -24889] [ -9050 6899] [ 61153 22443] [141347 51874] [119508 53911] [ 50141 22619] [ 33487 -20748] [-159796 99007] [ -24949 -43135] [ -95015 -164274] [ 41491 49159] [136653 161908] [-172876 -486351] [ -53453 -150379] [-1206903 -1560320] [ -740830 -957767] [4352921 7025200] [1826552 2947881] [ -8154983 -1731786] [-13279521 -2820029] [ -55507619 -150310996] [ -23410563 -63394271] [-51568157 -13597172] [-94871257 -25015065] [270779912 195819865] [ 71735207 51876738] [-17180080 -7458563] [-54165733 -23515521] [ 124560166 -220672329] [ -33770973 59829073] [-4785913344105250 -1819868390249059] [-1713809634997161 -651685009189966] [ 96511 155701] [ 28275 45616] [ -28652104 -7763365] [-101781395 -27577944] [ 120929027 -198413576] [-170278202 279382939] [299839807 686557654] [125546750 287470443] [2152835803 2929165420] [1685641743 2293497487] [ -30433450613 -11616452002] [-102869570742 -39265328345] [-165501292019 -130344294769] [ -93410305795 -73567404124] [377888654221 600623181828] [208263657964 331018090933] [254009873356 90361069155] [106357190625 37835338171] [223290353743 131025702488] [289323562789 169773671031] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ -189600040499 171153652163] [ 1283927279299 -1159012637262] [133760019715795 36184722421542] [226925540441902 61387832542903] [-1689047129627949 -353966813508403] [-2676580208439023 -560920148918230] [ -8736208920539365 -4793794462819056] [-11319758645326944 -6211458174590701] [443183243763048251 269543640732813260] [129843721932092630 78970832107063051] [ 93110983965335882 424947922704610521] [120646662033554301 550617620274432671] [ 96511 155701] [ 28275 45616] [11030014 14261585] [17795935 23009784] [-79759370 -48509599] [-63024851 -38331675] [-814321208 -502708269] [-513565899 -317041754] [-115407588 -278510801] [ -68261023 -164732948] [ 12051214 -7763365] [-68579615 44178834] [ 1887418961 -2609624160] [-1169831520 1617457841] [ -23161878647 -62637026690] [ -38001847530 -102768984083] [ -4576031066 12877729887] [ 6466870801 -18198874568] [ 90863983377 157650135328] [148339316636 257370549617] [1553203172859 651883265866] [ 857859946748 360045970491] [1507405651883 930611890372] [2397395435168 1480055945859] [ 1771682892253 6401823709281] [ 6401823709281 23132439210154] [-422208792523 -720969423744] [-366690223699 -626165167459] [40421042605832 11819613051361] [22157328613751 6479077074291] [-21373163627884896 -77230264272481879] [ -6181330209382457 -22335755901070849] [-764626478501469191 -142958361931163588] [-482176485603612139 -90150109212422763] [ 43601 -27040] [-113906 70641] [ 96511 155701] [ 28275 45616] [3744459 6066775] [1553057 2516264] [-49187116 -14434027] [-21588101 -6335058] [-71210004 -27597293] [-51293995 -19878884] [-556034950 -676113499] [-391517001 -476067070] [3642246233 2616524908] [2575513553 1850203125] [13864609788 17926242517] [ 4133125631 5343923381] [-65282806619 -11616452002] [-24817135920 -4415972339] [178157546774 69057145767] [255757513443 99136321793] [ -63059095805 -165998433112] [ -18500415202 -48700982725] [377888654221 600623181828] [208263657964 331018090933] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ -410631388651671 -595674476929820] [-1079902353575380 -1566539449683831] [ -8855917065681319 -5242843850357821] [-30564340401416227 -18094575968285672] [443183243763048251 269543640732813260] [129843721932092630 78970832107063051] [ 96511 155701] [ 28275 45616] [-171697666 -61031881] [ -71891651 -25554702] [ -28652104 -7763365] [-101781395 -27577944] [ 120929027 -198413576] [-170278202 279382939] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 390162579 287247368] [2556387172 1882075643] [-14975211813 -4390281500] [-50618446399 -14839805377] [26851309720 91834502461] [15055143459 51490285705] [ 1193989689 1693734257] [ 7701803140 10925394029] [377888654221 600623181828] [208263657964 331018090933] [354316056231 131025702488] [104781177589 38747968543] [ -884493238309 -537919581411] [-2029936942021 -1234540619248] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [146558100731500 30713591517213] [232246042695723 48670868762920] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [ 2293661036527830 -1859165218337483] [-15532137896754793 12589833495093094] [3835547694877838 5424947657192695] [5045336062867871 7136056237954467] [ 1 0] [15 1] [ 1103 -782] [-1426 1011] [3070 5229] [2241 3817] [680679 183736] [835856 225623] [1625641 470139] [1997903 577798] [-1301394 -349379] [-4622953 -1241102] [3624470 2145493] [1078413 638363] [ 244441 1028280] [ 135300 569161] [ 72323300 124475819] [ 16291521 28039379] [ -7010124 -31199297] [-10874923 -48399993] [ 5379251 23888308] [ 7467782 33163107] [ 4929557 -17498216] [ -1350094 4792365] [98250298 59755109] [77673803 47240636] [-316035455 -195471987] [-511443922 -316334633] [265305689 145152540] [838659120 458842409] [-16080706644 -10179256465] [-39223240907 -24828724099] [ 26955173615 -7593753489] [-44319502311 12485594792] [189569987571069 73521968583403] [295251990456617 114509199713908] [-1 0] [15 -1] [ 1 0] [-18 1] [ 1 20] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-30 1] [ 1 0] [-32 1] [-1 0] [33 -1] [ 1 0] [-39 1] [ 1 0] [-40 1] [ 1 0] [-50 1] [ 1 0] [-51 1] [-1 0] [54 -1] [ 1 58] [ 0 1] [-1 0] [58 -1] [-1 0] [63 -1] [-1 0] [64 -1] [-1 0] [14 -1] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-30 1] [ 1 34] [ 0 1] [ 1 0] [-38 1] [ 1 0] [-39 1] [-1 0] [39 -1] [-1 0] [39 -1] [ 1 0] [-47 1] [ 1 0] [-59 1] [ 1 0] [-71 1] [-1 0] [14 -1] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-30 1] [-1 0] [36 -1] [ 1 0] [-36 1] [-1 0] [41 -1] [ 1 0] [-42 1] [-1 0] [43 -1] [-1 0] [44 -1] [ 1 0] [-45 1] [-1 0] [52 -1] [-1 0] [54 -1] [-1 0] [15 -1] [ 1 0] [-20 1] [ 1 28] [ 0 1] [ 1 0] [-28 1] [ 1 0] [-29 1] [ 1 29] [ 0 1] [ 1 0] [-30 1] [ -1 -34] [ 0 -1] [-1 0] [34 -1] [ 1 0] [-35 1] [-1 0] [37 -1] [ 1 0] [-38 1] [-1 0] [38 -1] [-1 0] [42 -1] [-1 0] [42 -1] [ 1 47] [ 0 1] [ 1 50] [ 0 1] [ 1 0] [-50 1] [ 1 0] [-53 1] [-1 0] [54 -1] [119508 53911] [ 50141 22619] [ -28652104 -7763365] [-101781395 -27577944] [304566037 370338610] [232528508 282744213] [-768210187 -450031145] [-285474407 -167235968] [-1377455834 -1962518153] [-3120103093 -4445339595] [ -30433450613 -11616452002] [-102869570742 -39265328345] [70760351569 13083129945] [86963016925 16078897654] [377888654221 600623181828] [208263657964 331018090933] [519689014502 179035774557] [217599477937 74964238205] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [ -3274648482745 -12335803273277] [ -618342945117 -2329336100218] [11737169792057 16175177172921] [27825395660092 38346612742469] [142859544220579 42233773454388] [102626213146903 30339535661935] [263495431404428 375412814766531] [145532904626725 207346734916292] [443183243763048251 269543640732813260] [129843721932092630 78970832107063051] [ 96511 155701] [ 28275 45616] [26788114 8297697] [70220393 21750973] [3480072226 789991961] [4927002143 1118451524] [ 33946776941 -21883589362] [-193380792609 124661786399] [ -52129121993 -15282546829] [-223789331158 -65607683431] [ 58844209777 94708555527] [ 80713681859 129907024822] [621396377215 142456821408] [235311099488 53945714047] [1214292963837 360234473807] [ 461524670038 136916791591] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ 775402698292 940501859587] [ 988381946101 1198828763864] [-4109006143063 -534283613366] [ -711914776043 -92568466853] [-46773243219289 -54983990652868] [-19715380804057 -23176291384493] [-42425308666113 -57724210506175] [-34287235896863 -46651484333602] [ 6230695433773880 16111432812040971] [ 9021054286030389 23326787766790319] [25186164334012655 7790490380127124] [68107440294887561 21066739317501723] [1071524935004122483 1299674604179330160] [ 224555222401510165 272367641906495947] [172941999006337318181038 417548862366684345376973] [ 36242758955026372314173 87504035212098377379035] [-1 0] [14 -1] [ -1 -15] [ 0 -1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 28] [ 0 1] [ 1 0] [-30 1] [-1 0] [31 -1] [-1 0] [33 -1] [-1 0] [34 -1] [ 1 0] [-35 1] [ 1 38] [ 0 1] [ 1 39] [ 0 1] [-1 0] [39 -1] [ 1 51] [ 0 1] [ 96511 155701] [ 28275 45616] [-10682725 6621216] [ 18470939 -11448397] [32191901 9413305] [ 6854317 2004286] [-344185829 -486421824] [-556996419 -787177133] [1617457841 1169831520] [2609624160 1887418961] [ 305829827 -1043859568] [ -415712460 1418911403] [1864786627 1134160551] [1468388122 893071549] [679213045 413010827] [442443292 269037633] [1368749015 2160368604] [ 972912276 1535598647] [71345974183 49676152271] [39347313561 27396404104] [-14975211813 -4390281500] [-50618446399 -14839805377] [ -20708788346 -116348294973] [ -12126527275 -68130532256] [ 763033442167 1078358940658] [1231086497406 1739836103947] [-474567330329 -180427802104] [-202034211446 -76812259065] [ -361602968819 -857600800639] [ -873049458221 -2070580108380] [-138759293718595 -52755602137496] [ -58098948240929 -22088934844403] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [-1 0] [14 -1] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-33 1] [ 1 0] [-34 1] [ 1 0] [-36 1] [-1 0] [36 -1] [ 1 0] [-54 1] [65597 53911] [93119 76530] [ 57511 207844] [ 20748 74983] [ 8393958 12153373] [13576397 19656879] [ 2707133 -9238170] [-11788142 40227377] [ -28652104 -7763365] [-101781395 -27577944] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 74928070698 21966449951] [253267910821 74249835014] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [-216246471482860 -814613772103393] [ -94159795682283 -354705747637177] [1715158468835377 3937505190792432] [ 740919046425614 1700934720765937] [ 16933581617178329 -10466120360526030] [-11796885764338215 7291288345265819] [2968313660048603657 2277339252456544015] [1755688518118373962 1346993220835282783] [-35500485091295159995 -25103160973556010521] [-21918290705147643519 -15498897505809947320] [ -1148953540481580461 3921251298592970966] [ 5021694208787621778 -17138486669436349409] [ 96511 155701] [ 28275 45616] [-10682725 6621216] [ 18470939 -11448397] [25337584 6854317] [32746603 8858603] [-344185829 -486421824] [-556996419 -787177133] [1617457841 1169831520] [2609624160 1887418961] [ 305829827 -1043859568] [ -415712460 1418911403] [1864786627 1134160551] [1468388122 893071549] [679213045 413010827] [442443292 269037633] [71345974183 49676152271] [39347313561 27396404104] [-14975211813 -4390281500] [-50618446399 -14839805377] [ -20708788346 -116348294973] [ -12126527275 -68130532256] [ 763033442167 1078358940658] [1231086497406 1739836103947] [ -69668710359 112849858622] [ 290548378870 -470632272499] [ -361602968819 -857600800639] [ -873049458221 -2070580108380] [139100237115220 52885227025421] [ 58243042708979 22143718804478] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [119508 53911] [ 50141 22619] [ 33487 -20748] [-159796 99007] [ 1554907 -1183263] [-1060680 807163] [-25088634 -15758545] [-40578545 -25487989] [ 5025543 26609315] [ 8839498 46803497] [143769737 330093545] [ 64958538 149144003] [-46414045 -25375702] [-81613097 -44619891] [ 220353995 -399080161] [-136547534 247299405] [ -50957877 -215926057] [ -22074482 -93537175] [-523983107 -236825177] [-847494330 -383042873] [-2348890897 664969439] [ 1317064986 -372860215] [ -3080338690 -2121266171] [-11746236639 -8089011283] [ 8443454353 5440326290] [18651858283 12017853207] [-1612389813 -618251824] [-2915239451 -1117814125] [-50058428276 -13393173575] [-10577700125 -2830072351] [ 2343967620 -14610012023] [ -8840977813 55106047985] [173258346313 47538336637] [583841134592 160193358585] [ 88051360399 144568436695] [123839229105 203327281624] [ 8038916071510 -2822351660427] [-13221252160207 4641797806489] [ 96511 155701] [ 28275 45616] [ -28652104 -7763365] [-101781395 -27577944] [ 120929027 -198413576] [-170278202 279382939] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 19791831799 -4315819386] [-35066512786 7646626003] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [254009873356 90361069155] [106357190625 37835338171] [ 24091937426 86915826289] [ 85534088277 308578999979] [ 530064318909 1812879534839] [ 297199479112 1016455615341] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ 3501321989573 -1570962722003] [-2243451109312 1006584961869] [ -345389284481 282192071278] [ 2338895725737 -1910938928927] [133760019715795 36184722421542] [226925540441902 61387832542903] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [955017288165885557 217614178145613918] [200139155232778487 45604533363351431] [-26380878693674228743 -62751699269476296356] [-15487752488971594035 -36840425136448262827] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [-1 0] [24 -1] [-1 0] [30 -1] [ 1 0] [-30 1] [ 1 0] [-34 1] [ 1 36] [ 0 1] [ 1 0] [-37 1] [-1 0] [41 -1] [ 1 0] [-41 1] [-1 0] [44 -1] [ 1 0] [-46 1] [-1 0] [52 -1] [-1 0] [60 -1] [ 1 0] [-15 1] [-1 0] [24 -1] [ 1 24] [ 0 1] [ 1 0] [-24 1] [ -1 -26] [ 0 -1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-29 1] [-1 0] [30 -1] [-1 0] [31 -1] [-1 0] [32 -1] [ -1 -35] [ 0 -1] [ 1 0] [-40 1] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-29 1] [ 1 0] [-31 1] [ 1 0] [-31 1] [ 1 0] [-32 1] [ 1 0] [-38 1] [ 1 0] [-42 1] [ 1 0] [-48 1] [ 1 0] [-48 1] [ 1 49] [ 0 1] [ -1 -60] [ 0 -1] [ 1 0] [-65 1] [ 1 0] [-15 1] [ 1 24] [ 0 1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 0] [-31 1] [ 1 0] [-31 1] [ 1 0] [-37 1] [ 1 39] [ 0 1] [-1 0] [45 -1] [-1 0] [48 -1] [-1 0] [48 -1] [ -1 -15] [ 0 -1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 0] [-32 1] [-1 0] [37 -1] [-1 0] [40 -1] [ -1 -41] [ 0 -1] [ 1 0] [-43 1] [ 1 0] [-44 1] [-1 0] [45 -1] [ 1 0] [-48 1] [ 1 0] [-49 1] [ 1 0] [-51 1] [-1 0] [14 -1] [ -1 -15] [ 0 -1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [-1 0] [27 -1] [-1 0] [27 -1] [ 1 0] [-29 1] [ 1 0] [-31 1] [ 1 0] [-32 1] [-1 0] [33 -1] [-1 0] [33 -1] [ 1 34] [ 0 1] [-1 0] [35 -1] [ 1 0] [-36 1] [ 1 45] [ 0 1] [-1 0] [48 -1] [ 96511 155701] [ 28275 45616] [ 12051214 -7763365] [-68579615 44178834] [ 80969363 130318538] [198413576 319342603] [ 63300425 -214479068] [-233514368 791210233] [-18753416456 -11405800987] [-14831696205 -9020616356] [-14975211813 -4390281500] [-50618446399 -14839805377] [ 33759396970 116495185273] [ 7690932653 26539473591] [-165501292019 -130344294769] [ -93410305795 -73567404124] [ -47315060585 -66939523811] [-199151485029 -281751844112] [254009873356 90361069155] [106357190625 37835338171] [377888654221 600623181828] [208263657964 331018090933] [223290353743 131025702488] [289323562789 169773671031] [ 530064318909 1812879534839] [ 297199479112 1016455615341] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ -987858985099 -2082186223899] [ -171153652163 -360753692662] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [-561993988911064299 -152030453752397986] [-865392724518220436 -234105793262051003] [ 72230061415495262290 102161238522326910673] [ 93664583065816723533 132477940959197686999] [-1 0] [15 -1] [ 1 18] [ 0 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 30] [ 0 1] [ 1 30] [ 0 1] [-1 0] [30 -1] [ 1 0] [-33 1] [-1 0] [35 -1] [ 1 0] [-37 1] [ -1 -39] [ 0 -1] [-1 0] [39 -1] [ 1 0] [-40 1] [ 1 51] [ 0 1] [ 96511 155701] [ 28275 45616] [ 107337 -73513] [-140261 96062] [ 5031733 1292264] [17874317 4590533] [212350319 80723124] [172230444 65471903] [ 234334241 413619382] [ 603531592 1065283345] [-18753416456 -11405800987] [-14831696205 -9020616356] [-350777034 -91395275] [-985646491 -256811089] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [120334732494509 205628578706521] [ 73187518576039 125063189254480] [ -330220265171428 -758431267745689] [ -523900826521663 -1203265849918586] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [ -870348302415853 2970826136481609] [ 3787814482207630 -12929235609066907] [ 8300294033183311 -3498613131310525] [-18548910168645691 7818453229256816] [ 84395688772766589 49964955551705081] [204248046901642006 120921396973730483] [ 60993630059966673849 21012646979452286051] [259847650563036404878 89518970167097861571] [-1 0] [14 -1] [ -1 -15] [ 0 -1] [ 1 24] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-32 1] [-1 0] [32 -1] [ 1 0] [-36 1] [-1 0] [36 -1] [ 1 39] [ 0 1] [ 1 0] [-40 1] [-1 0] [41 -1] [ -1 -15] [ 0 -1] [-1 0] [22 -1] [ 1 24] [ 0 1] [ 1 0] [-27 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [-1 0] [30 -1] [-1 0] [32 -1] [-1 0] [33 -1] [ 1 34] [ 0 1] [ 1 36] [ 0 1] [ 1 44] [ 0 1] [ 1 51] [ 0 1] [ 96511 155701] [ 28275 45616] [680679 183736] [835856 225623] [ -28652104 -7763365] [-101781395 -27577944] [1121599769 -866082604] [-792993337 612337621] [1447396154 880304481] [1777353201 1080983933] [1345415226 1742710699] [1951315715 2527531061] [12747111812 20260493947] [ 7040411329 11190159247] [5675139455 4077551847] [2351754772 1689720947] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 8798521485 -23797243919] [-23725984696 64171354925] [-351749262001 -103160365006] [-846629736682 -248297984093] [-366493233369 -126227904536] [-153455389339 -52853232945] [-9027781532330 -2436854258101] [-4073789193519 -1099631233574] [33174830492492 47075911535101] [ 7451692339323 10574137204172] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [8060902983716557 2989297213109146] [2392100313702518 887084091654897] [-1535740868299096 678068932895255] [ 5575686346956497 -2461808348974091] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 20] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ -1 -27] [ 0 -1] [ 1 28] [ 0 1] [ 1 0] [-31 1] [ 1 0] [-35 1] [ 1 0] [-36 1] [-1 0] [43 -1] [ -1 -50] [ 0 -1] [-1 0] [78 -1] [ 1 0] [-15 1] [-1 0] [24 -1] [ 1 24] [ 0 1] [ -1 -30] [ 0 -1] [ 1 0] [-31 1] [ 1 0] [-33 1] [ 1 0] [-34 1] [ -1 -35] [ 0 -1] [ 1 36] [ 0 1] [-1 0] [36 -1] [ -1 -37] [ 0 -1] [ 1 0] [-41 1] [ 1 0] [-44 1] [-1 0] [54 -1] [ 1 0] [-105 1] [1576 2241] [3735 5311] [ 96511 155701] [ 28275 45616] [5615771 6828523] [4380785 5326836] [-11506976 -6998275] [ -3371349 -2050376] [ 12051214 -7763365] [-68579615 44178834] [ 12439200 -41725747] [-52670117 176675347] [-457818327 -135369964] [-593126162 -175378447] [ 73353565 12509078] [313103333 53393915] [164553641 28110027] [ 75802320 12949001] [-1569712957 -460187839] [-4978628064 -1459568821] [-22956920614 -14468161601] [-59861837773 -37726782141] [ -55018310829 -156491426389] [ -33460840790 -95174399659] [168592696176 287808118057] [475476840695 811696460191] [-418848900501 -79348532765] [-146929973944 -27835044661] [1381060621973 1019551933073] [ 522298395383 385580712520] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ 8201998096049 -27995091938880] [-30437920433580 103890828916049] [ -1 -15] [ 0 -1] [ 1 24] [ 0 1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 31] [ 0 1] [ 1 0] [-32 1] [ -1 -34] [ 0 -1] [ 1 37] [ 0 1] [ 1 0] [-37 1] [-1 0] [38 -1] [ 1 39] [ 0 1] [-1 0] [42 -1] [ 1 0] [-42 1] [ 1 0] [-51 1] [ 96511 155701] [ 28275 45616] [ 7428104 19412705] [10182735 26611694] [-79759370 -48509599] [-63024851 -38331675] [24833600 11544117] [ 9795747 4553639] [-134094214 -346864077] [-105028059 -271678096] [ -28652104 -7763365] [-101781395 -27577944] [ 447626321 1169831520] [1169831520 3057250481] [3397882399 1964894400] [5414004000 3130757599] [-17393327105 -47037017981] [-28537346974 -77173946919] [113222833717 46175967588] [270314819918 110243207605] [-6393318853353 -1186249398760] [-3708976463771 -688182648337] [51743922136627 92271875984497] [31944520865454 56964774720757] [10114028798926368 3845296273015475] [ 7157056349473189 2721072151713907] [ 1 0] [15 1] [1011 1426] [ 782 1103] [3070 5229] [2241 3817] [ -83011 -37108] [-204040 -91211] [-647555 -175328] [-177678 -48107] [1648329 2849045] [4352740 7523469] [ -766749 -1332250] [-2465855 -4284499] [ 391664 -252095] [-1688545 1086834] [ 390248 1769679] [ 220473 999791] [ 298561 1136520] [ 135300 515041] [ -61782375 -106949324] [ -13917076 -24091367] [77430935 47093419] [61200391 37222018] [13888233971 17116452343] [33096630921 40789700624] [-2341584388884 -1452029110985] [-7427739534859 -4605981353749] [-369896726266184 -234038860649343] [-597958493547841 -378336748092296] [ 1 0] [15 1] [ 70641 113906] [ 27040 43601] [16051 42277] [ 3827 10080] [ 96511 155701] [ 28275 45616] [ 45712 61883] [108413 146765] [388747 286856] [502642 370899] [ 33557 -40873] [-223088 271725] [-750631 -441025] [-611910 -359521] [158241 71645] [507745 229886] [ -8759393 -12113145] [-19427485 -26865782] [16924621 22914606] [ 4959240 6714421] [-328248843 -209439842] [-207805558 -132590759] [ -15766934 -66395575] [ -26523327 -111691439] [ 477735549 1218819773] [ 144277132 368086113] [ -253105990 -407940873] [ -803093483 -1294377334] [5912447169 3648855284] [2104900984 1299035553] [ 11265744551 -17439935025] [-15392591700 23828500451] [-23700809894 -13448077803] [-30731020537 -17437089998] [28981033802 93122048207] [10298581441 33091469544] [-29046047434278 -18405956818811] [-47427212346475 -30053769775767] [-1 0] [15 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 0] [-28 1] [ 1 0] [-34 1] [ -1 -38] [ 0 -1] [ 1 0] [-39 1] [-1 0] [45 -1] [ 1 0] [-46 1] [ -1 -15] [ 0 -1] [ 96511 155701] [ 28275 45616] [-176029 -127744] [-282813 -205237] [730389 213992] [309304 90621] [-709699 -196735] [-260630 -72249] [1936616 3336435] [1141477 1966556] [-2754988 7247309] [ 996079 -2620299] [ 3818637 20695774] [ 5270258 28563089] [ -7879246 -13449627] [ -3554635 -6067651] [ 71228909 -30918933] [-90856157 39438698] [ 97181555 54978456] [137114664 77569787] [155831859 59758790] [406359772 155831859] [ 271303569 1026815315] [ 385360945 1458493604] [-234368138 -84800693] [-611153687 -221131834] [353644162 254500107] [307044539 220964677] [-3455772447 -8816995021] [-2119022891 -5406436496] [ 64276510304 -49302124305] [-40375588047 30969358034] [ 244374940285 632292961997] [ 443661156622 1147923868611] [1423828462999 1969845590222] [5143411996088 7115834317463] [ 1 0] [-15 1] [ 1 24] [ 0 1] [ 1 0] [-44 1] [ 1 0] [-45 1] [ -1 -45] [ 0 -1] [ 1 0] [-46 1] [ -1 -46] [ 0 -1] [ 1 52] [ 0 1] [ 1 0] [-53 1] [ 1 53] [ 0 1] [ 1 57] [ 0 1] [ 1 0] [-58 1] [ 1 0] [-63 1] [-1 0] [63 -1] [ 96511 155701] [ 28275 45616] [ -4827181 -12615395] [ -6621216 -17303941] [ -28652104 -7763365] [-101781395 -27577944] [1617457841 1169831520] [2609624160 1887418961] [ 305829827 -1043859568] [ -415712460 1418911403] [-18753416456 -11405800987] [-14831696205 -9020616356] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [7026765169307 4272476547299] [4577264882191 2783109494730] [ 1284412385559 -3559924551547] [ -930410296820 2578759357899] [15471776798113 4185421110286] [55906093039056 15123702019009] [ 90749487323730 146774366979833] [ 26930218732693 43555792144799] [-150887201219573 -34374353300878] [ -98288821615896 -22391658486893] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [290434359244676143 688809992343382900] [352273800693151601 835471789871129307] [ -1 -15] [ 0 -1] [119508 53911] [ 50141 22619] [ 33487 -20748] [-159796 99007] [-2424368 548049] [ 6587631 -1489190] [ -2472261 3579055] [ 11797844 -17079561] [17930735 21742308] [46263708 56098079] [ 47015833 107934679] [ 21223055 48721962] [ 397080487 -75762642] [-547505237 104463565] [-350018968 -476855705] [-566122855 -771269382] [22294762328 28532154513] [31391533975 40173924467] [-2673856522160 -1090766075413] [-3770006276083 -1537926555133] [-10713579470023 -4369389502361] [-15105419054142 -6160542293881] [24285684292585 62794397511918] [ 9955903644573 25742530600159] [817579189106929 311013389986899] [338793919988679 128879803897318] [-1944618769528406 -762152477642175] [ -701500874089239 -274938531723071] [-1853819066819287 1148769946470307] [ 707258776115851 -438272343251534] [5587774113940701 3269145081955946] [3267566168140480 1911700016987381] [ 1298521755435668 5726982048981829] [ 3129373603378467 13801745235368108] [475233007318527006 293427547745722315] [669274813155141365 413236589563027996] [ -1 -15] [ 0 -1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 0] [-31 1] [-1 0] [32 -1] [-1 0] [35 -1] [-1 0] [37 -1] [-1 0] [38 -1] [-1 0] [40 -1] [ 1 42] [ 0 1] [ 1 0] [-44 1] [-1 0] [45 -1] [ 1 0] [-48 1] [ 1 0] [-51 1] [ 1 0] [15 1] [3817 2241] [5229 3070] [47443 68847] [19663 28534] [10544507 6454773] [12927718 7913645] [ 13942034 -24042609] [-21639861 37317275] [ 44561594 165983525] [ 18411357 68578829] [101892591 160964248] [ 84409058 133344735] [790141257 445636028] [609823282 343937521] [ 959437839 1752985034] [ 751424293 1372924317] [-3559355997 5165894507] [ 6066470332 -8804611225] [65892810255 25818741676] [46627028084 18269841407] [ 24976596479 -38766948935] [-85249848145 132318929544] [225732607583 65388003623] [158950600967 46043248174] [ 436353964835 -1925474837511] [ -180323761994 795704621261] [912516228640 714886951719] [493346411881 386499331696] [-16036881589139 -8783868948650] [ -6645014838438 -3639668920559] [ -3613826911847 -6172029044587] [-12221693180074 -20873342061337] [178974636152404 129494553595829] [291434940604511 210863608090655] [10630150474585309642797 25652322557922930167801] [17139856690348259645197 41361327242598516411134] [ -1 -14] [ 0 -1] [-1 0] [15 -1] [ 1 0] [-24 1] [-1 0] [24 -1] [ 1 0] [-24 1] [-1 0] [26 -1] [ 1 27] [ 0 1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [-1 0] [30 -1] [-1 0] [31 -1] [ 1 36] [ 0 1] [ 1 36] [ 0 1] [-1 0] [40 -1] [ 96511 155701] [ 28275 45616] [ -28652104 -7763365] [-101781395 -27577944] [152714741 48769386] [197898792 63198893] [3315472894 694822855] [5914725319 1239547559] [11844592315 26959531689] [ 5304487286 12073568197] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 5315452571 -20048188663] [-14333583950 54061698681] [54392214787 11398962862] [15935818251 3339665449] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [ 51686413294231 -22826703913392] [-70257323435554 31028330611399] [17800882949666 23015627214239] [10776429734145 13933370056016] [ 49873062635480 -64627766012149] [-168562649311691 218431090501227] [-371595688729283 -100684782147922] [-662626557234738 -179540324562839] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [ 6940164253133958 -23669337231695633] [-26658316645215433 90917831868315855] [ 1 0] [-15 1] [ 1 0] [-20 1] [ -1 -26] [ 0 -1] [-1 0] [27 -1] [ 1 30] [ 0 1] [ 1 0] [-30 1] [ 1 0] [-32 1] [ -1 -33] [ 0 -1] [ 1 0] [-37 1] [-1 0] [41 -1] [-1 0] [44 -1] [ 1 0] [-45 1] [ 1 0] [-51 1] [ 1 0] [-54 1] [ 1 0] [-58 1] [ 1 0] [15 1] [1885 552] [ 782 229] [3070 5229] [2241 3817] [ 313207 1011024] [ 183736 593095] [-1301394 -349379] [-4622953 -1241102] [-4542969 -1217795] [-3298885 -884304] [ 244441 1028280] [ 135300 569161] [-32069005 -18987137] [-39422807 -23341112] [ 5379251 23888308] [ 7467782 33163107] [98250298 59755109] [77673803 47240636] [1054675313 238488102] [ 400910838 90655829] [2253643407 800913889] [1322053271 469839560] [265305689 145152540] [838659120 458842409] [-46392487334 -79220153121] [-28638688223 -48903634976] [-14517619514 -9189824939] [-35410638363 -22415353097] [ -65985126049 -40917693912] [-209311302177 -129794944825] [ 642896728928 194699949305] [1037257086807 314131170887] [-1 0] [14 -1] [ 1 15] [ 0 1] [-1 0] [24 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-27 1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-36 1] [-1 0] [36 -1] [-1 0] [40 -1] [-1 0] [45 -1] [-1 0] [48 -1] [ 1 0] [-50 1] [ 96511 155701] [ 28275 45616] [-2060725 -1306387] [ -862852 -547001] [ 1542841 -4215120] [-2107560 5757961] [ -7380436 -1999749] [-17490223 -4739023] [34288748 47032387] [43475277 59633150] [-200275829 -58737442] [-676961697 -198541175] [496269245 301827424] [392268326 238574805] [ 1884926440 -3198072287] [-2973219097 5044530861] [260706007243 368739101916] [190916359992 270029555011] [377888654221 600623181828] [208263657964 331018090933] [ -81563865153 -49553556293] [-103415562847 -62829402524] [ 454198788424 -1550273523735] [-1678985648505 5730722018524] [-1859645762425 -2569451818082] [-1099936919057 -1519770578651] [ 500192860049 -1707260762782] [-2148751311412 7334128685065] [ -31136573570012 -117293389491489] [ -5879434296819 -22148190950291] [443183243763048251 269543640732813260] [129843721932092630 78970832107063051] [ 1 0] [-15 1] [-1 0] [24 -1] [ 1 24] [ 0 1] [-1 0] [30 -1] [ 1 0] [-30 1] [-1 0] [32 -1] [ 1 0] [-34 1] [-1 0] [35 -1] [-1 0] [41 -1] [ 1 0] [-41 1] [ 1 0] [-41 1] [-1 0] [43 -1] [ 1 44] [ 0 1] [ 1 56] [ 0 1] [ 1 0] [-15 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-29 1] [ 1 0] [-31 1] [ 1 37] [ 0 1] [ -1 -38] [ 0 -1] [-1 0] [43 -1] [ 1 0] [-45 1] [ 1 51] [ 0 1] [ 1 0] [15 1] [65597 93119] [53911 76530] [ 78259 204568] [ 20748 54235] [ -7936617 -11491202] [-12836533 -18585651] [-43066064 -11650005] [-27763955 -7510559] [40535251 65996595] [49786905 81059476] [ -28652104 -7763365] [-101781395 -27577944] [ 588673408 -102073383] [-852914537 147891634] [-2299739648 -2796380015] [-1798928497 -2187416172] [-1223457231 -2084982494] [-3167540533 -5398036313] [64312583775 20023835558] [26928477553 8384228633] [165654669332 48564473775] [559930649665 164153159468] [-4007643877921 -5181802480205] [-1489451779336 -1925831026761] [ 94431630417 112548760088] [310961472994 370620819169] [-202308707787 -857880843112] [-124167334397 -526525915195] [443183243763048251 269543640732813260] [129843721932092630 78970832107063051] [ 1 0] [15 1] [65597 93119] [53911 76530] [ 16015 89908] [ 20748 116479] [ -7936617 -11491202] [-12836533 -18585651] [-43066064 -11650005] [-27763955 -7510559] [ 88006486 -52102575] [-56733915 33588241] [6027706057 3468544341] [2766368337 1591861174] [ 7766834369 4192912928] [19821815299 10700774817] [-65351109870 -39746451257] [-51871740427 -31548318102] [292034710475 119141089017] [ 62180188472 25367585099] [ -95485999290 -36451571993] [-264228956353 -100868827857] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ -817653570743 -247026718456] [-3150022308084 -951674036135] [-25137222281735 -57734898016678] [-11504911307173 -26424354829897] [-5790274011419544 -9208793950505441] [-2608932444375007 -4149220099714752] [13374997084270694 4136873604496965] [36168056404074713 11186744708896709] [304117493418743291 483369941193670630] [137180104259175340 218036582451368011] [ 129816456076611577104 -89474684126410593329] [-221598557487782838127 152734572590599545796] [-4176051764184078387635 -2582053190684690616831] [-2459649305862244000524 -1520801392510479655607] [-3074590806995317057089 -1168777269984690307898] [-4459913870696268428212 -1695395025022325561993] [ 96511 155701] [ 28275 45616] [ 45009 76850] [198244 338489] [-1134681 -705086] [-2690155 -1671651] [3168675 8193649] [1430201 3698254] [-5492363 4482678] [ 9740198 -7949615] [-550803981 -203466230] [-211204528 -78018661] [3254273519 1429722965] [1334081120 586111279] [904099685 510779283] [370629483 209390474] [ -801282659 -474401202] [-1929461930 -1142342279] [ 331155105 1128466513] [ 137184188 467478109] [-1450417007 -392994009] [-6438906349 -1744637306] [ 7412164909 10254286921] [12677098385 17538007554] [ 12999935074 -31371953511] [-31461697605 75924603394] [502897671192 815652959405] [205085780779 332629943638] [ -56960790551 193962858093] [ 249959424405 -851161718366] [ 675120430535 -1816535652789] [-1775947869996 4778514287867] [2459909451760 3479263147587] [6447828121317 9119722170433] [10615707488369 15015859751893] [ 6578012752577 9304562794998] [ 1 0] [15 1] [36569 11369] [15195 4724] [11966 9911] [33301 27582] [65597 93119] [53911 76530] [ -280300 506973] [ 759863 -1374349] [ 2771850 13091417] [ 6363097 30052837] [ -4795207 -2803831] [-21185489 -12387480] [ 4058879 -2992820] [-6864460 5061519] [ 3058721 4474080] [10561410 15448481] [-29333111 -39784393] [ -6147087 -8337272] [23370485 29457938] [56223713 70868647] [ 668919962 489053587] [1617638907 1182670805] [-1008900092 -2247837649] [ -699906859 -1559398201] [2185532814 1257621413] [2591535931 1491247836] [-14075737992 -4109946277] [-19848453851 -5795509909] [-18493092661 13644768500] [ 50107640653 -36970947441] [ 106326487871 -65556857486] [-260375641709 160537690825] [-1678716147324 -7097625728735] [ -693224110765 -2930957262899] [-4458206480005351 -5431391983309301] [-3599519296757489 -4385261279363690] [ 1 0] [-15 1] [-1 0] [24 -1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-26 1] [ -1 -26] [ 0 -1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-36 1] [ 1 0] [-36 1] [ 1 0] [-40 1] [ 1 0] [-51 1] [ 96511 155701] [ 28275 45616] [ 5213849 -17795935] [ -8445420 28825949] [-79759370 -48509599] [-63024851 -38331675] [-134094214 -346864077] [-105028059 -271678096] [-814321208 -502708269] [-513565899 -317041754] [ 12051214 -7763365] [-68579615 44178834] [-115407588 -278510801] [ -68261023 -164732948] [ 1887418961 -2609624160] [-1169831520 1617457841] [2598447199 9385243200] [1088133600 3930192799] [ 17526634969 -46099176084] [-24769328896 65149166185] [ -4576031066 12877729887] [ 6466870801 -18198874568] [ -23662683727 -109165997601] [ -6981116798 -32206853137] [ 90863983377 157650135328] [148339316636 257370549617] [161342687479 274978803926] [101508850352 173003082407] [1507405651883 930611890372] [2397395435168 1480055945859] [160926336235033 275055622270441] [260767533378914 445704400159275] [ 422867514864285 1446070200775526] [ 584395629518344 1998444135821477] [ 96511 155701] [ 28275 45616] [ -28652104 -7763365] [-101781395 -27577944] [ 120929027 -198413576] [-170278202 279382939] [-18753416456 -11405800987] [-14831696205 -9020616356] [ -9751385343 -5774512595] [-16543346845 -9796532632] [16278264775 42093646834] [ 4315819386 11160193027] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [254009873356 90361069155] [106357190625 37835338171] [ 24091937426 86915826289] [ 85534088277 308578999979] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ 530064318909 1812879534839] [ 297199479112 1016455615341] [ 3501321989573 -1570962722003] [-2243451109312 1006584961869] [ -345389284481 282192071278] [ 2338895725737 -1910938928927] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [507723036982204056 116413012389610433] [106401474197708863 24396206655647280] [955017288165885557 217614178145613918] [200139155232778487 45604533363351431] [ 1 0] [15 1] [1576 2241] [3735 5311] [-1565 -5336] [-2024 -6901] [-22961 -6231] [-18060 -4901] [ 96511 155701] [ 28275 45616] [ 17341 76531] [ 28275 124786] [ 882152 261987] [1367757 406205] [2696371 640221] [2211714 525145] [-5604736 -2170649] [-1668439 -646167] [-5082801 3242779] [ 1543526 -984755] [ 3342177 4531448] [ 9443506 12803857] [-232443809 -101407545] [ -85132260 -37140389] [212350319 80723124] [172230444 65471903] [ 8391913 -14245916] [-48591273 82487413] [32466274 7313287] [17661981 3978502] [ 863123699 1220738571] [1576486263 2229666026] [-17739892347 -7994077616] [-30729134524 -13847383155] [-185218186387 -70299170424] [-149537969431 -56756819635] [-255828518239 -60796602697] [-315775847748 -75042840763] [ 128225032724 -337836064997] [-158323582699 417137083446] [-3726256644019 -2400771527412] [-2153640092962 -1387558160755] [ 589590114445 3398010745291] [ 366233591254 2110730230847] [23203714675947 18254857104112] [14593009126649 11480631443987] [120158073168285 155367694790069] [ 97359854899921 125888971269630] [-233 -377] [-377 -610] [ 1 0] [15 1] [1103 1426] [ 782 1011] [3070 5229] [2241 3817] [ 6901 2000] [10700 3101] [-21009 -16087] [ -3308 -2533] [ -4469 3308] [ 25767 -19073] [ 78259 20748] [204568 54235] [ -40667 -137559] [ -68769 -232616] [-66829 -93190] [-37003 -51599] [312573 554756] [219556 389669] [ -924449 -1600688] [ -563515 -975729] [-163933 -537785] [-133065 -436522] [ -791939 -1225440] [ -608184 -941099] [ 847461 -1428227] [ -267157 450240] [-1220166 -2111267] [ -662575 -1146461] [ -9281801 -10956550] [-12832658 -15148101] [152854891 270636040] [119711062 211953491] [-1 0] [14 -1] [ -1 -15] [ 0 -1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [-1 0] [24 -1] [-1 0] [26 -1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-28 1] [-1 0] [32 -1] [ 1 0] [-35 1] [ 1 0] [-38 1] [-1 0] [39 -1] [-1 0] [39 -1] [-1 0] [47 -1] [ -1 -48] [ 0 -1] [ 1 0] [-15 1] [ 1 0] [-24 1] [-1 0] [24 -1] [ 1 0] [-26 1] [-1 0] [26 -1] [ 1 27] [ 0 1] [ 1 28] [ 0 1] [ 1 0] [-44 1] [-1 0] [49 -1] [ 1 0] [-52 1] [ 1 54] [ 0 1] [ -1 -54] [ 0 -1] [ 1 0] [-60 1] [ -1 -81] [ 0 -1] [ -1 -15] [ 0 -1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 0] [-27 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-30 1] [ 1 0] [-32 1] [ 1 0] [-38 1] [ 1 0] [-38 1] [-1 0] [43 -1] [ 1 46] [ 0 1] [-1 0] [53 -1] [-1 0] [53 -1] [ 1 0] [-67 1] [ 1 0] [-69 1] [ 1 0] [-15 1] [ 1 24] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 0] [-28 1] [-1 0] [31 -1] [ 1 0] [-36 1] [ -1 -38] [ 0 -1] [ 1 0] [-40 1] [ 1 0] [15 1] [ 96511 155701] [ 28275 45616] [-435709 -702905] [-267197 -431054] [680679 183736] [835856 225623] [-53548316 -22180731] [-20355917 -8431808] [-222894675 315289918] [ 50502293 -71436717] [268269149 185161371] [329425611 227372018] [ 157875789 -415316257] [ -84798860 223076289] [ -470320065 1135001069] [ 1605851281 -3875324606] [3864943841 2285038009] [5995146926 3544459935] [ 3775680545 -9111476064] [-20337820626 49079249057] [ 3482757671 2655978468] [14476352895 11039780891] [11713084702 28653207145] [ 9059591029 22162081553] [-45500822952 28279664435] [ 80691494101 -50151364918] [ -82755550165 -17011290217] [-199674843422 -41045303955] [-3396403033787 -2401225528419] [-5385844301778 -3807742102709] [ 7468803332211 -32759568896648] [ -2682716022100 11766894433691] [-30382871404790 -23073283098561] [-73519972481389 -55832350927637] [-5655966075553753 -3343928645061864] [-6945339064959999 -4106233654648129] [3160975743898409445821 7248053170295731477530] [1309318965364717646955 3002241790737723606731] [-1 0] [14 -1] [ 1 15] [ 0 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 28] [ 0 1] [ 1 0] [-28 1] [-1 0] [29 -1] [-1 0] [34 -1] [ 1 0] [-38 1] [ 1 0] [-42 1] [ -1 -61] [ 0 -1] [-26833 -34709] [ -9829 -12714] [ 43601 -27040] [-113906 70641] [119508 53911] [ 50141 22619] [ 99007 159796] [ 20748 33487] [310261 63954] [791885 163231] [ 1092344 -1431897] [ -664479 871031] [-45538229 -13556655] [-16924495 -5038394] [ 8393958 12153373] [13576397 19656879] [ -273151415 -706348816] [ -608818469 -1574358327] [ 735623305 1276878603] [ 288685903 501094582] [14401305247 5478347622] [ 5967704842 2270152675] [2047296941 2806514568] [2895669966 3969497429] [-5882298661 3243354473] [15401465240 -8491988261] [ 40734870304 -98303577205] [-65883170243 158992805529] [ 34391587983 -21686116177] [-88733403524 55952138603] [-88465921073 -62556166632] [-19874299668 -14053547249] [-65351109870 -39746451257] [-51871740427 -31548318102] [-1032910977659 -2806978586895] [ -197386421563 -536405818754] [-566368739356397 -215115230901461] [-234697229154146 -89141481747031] [ 96511 155701] [ 28275 45616] [ 12051214 -7763365] [-68579615 44178834] [ 80969363 130318538] [198413576 319342603] [ 63300425 -214479068] [-233514368 791210233] [-18753416456 -11405800987] [-14831696205 -9020616356] [-14975211813 -4390281500] [-50618446399 -14839805377] [ 33759396970 116495185273] [ 7690932653 26539473591] [-165501292019 -130344294769] [ -93410305795 -73567404124] [ -47315060585 -66939523811] [-199151485029 -281751844112] [254009873356 90361069155] [106357190625 37835338171] [377888654221 600623181828] [208263657964 331018090933] [223290353743 131025702488] [289323562789 169773671031] [ 530064318909 1812879534839] [ 297199479112 1016455615341] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ -987858985099 -2082186223899] [ -171153652163 -360753692662] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [-561993988911064299 -152030453752397986] [-865392724518220436 -234105793262051003] [ 72230061415495262290 102161238522326910673] [ 93664583065816723533 132477940959197686999] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 0] [-28 1] [ 1 0] [-30 1] [-1 0] [33 -1] [-1 0] [34 -1] [-1 0] [40 -1] [ 1 0] [-42 1] [ 1 44] [ 0 1] [ 1 0] [-51 1] [ -1 -14] [ 0 -1] [-1 0] [15 -1] [ 1 0] [-24 1] [-1 0] [24 -1] [ 1 0] [-24 1] [-1 0] [26 -1] [-1 0] [27 -1] [ 1 0] [-28 1] [-1 0] [30 -1] [-1 0] [31 -1] [ 1 36] [ 0 1] [ 1 0] [-36 1] [-1 0] [40 -1] [ 96511 155701] [ 28275 45616] [26788114 8297697] [70220393 21750973] [ -28652104 -7763365] [-101781395 -27577944] [2152835803 2929165420] [1685641743 2293497487] [-59118636169 -20990309020] [-24753731334 -8788911649] [ 74928070698 21966449951] [253267910821 74249835014] [ 49193342963 -80713681859] [-85057688713 139557891636] [621396377215 142456821408] [235311099488 53945714047] [1214292963837 360234473807] [ 461524670038 136916791591] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ 775402698292 940501859587] [ 988381946101 1198828763864] [178777460839951 226176323631666] [231813924404796 293274224514487] [-312714891084395 -96727803247037] [-845631374884517 -261567541493494] [-211539085964897 -124130073312081] [-274097154018824 -160838833484585] [ -20139777086747 16324380645678] [ 136381875935321 -110544900589037] [218963293856347 310907254441867] [337173075119518 478754010368081] [24272804005834658 14219400333952293] [ 9021054286030389 5284679194729541] [-282978199489471079 -64238152320096691] [-165448510959904925 -37558040397988344] [ 96511 155701] [ 28275 45616] [26788114 8297697] [70220393 21750973] [ -28652104 -7763365] [-101781395 -27577944] [-59118636169 -20990309020] [-24753731334 -8788911649] [ 74928070698 21966449951] [253267910821 74249835014] [ 49193342963 -80713681859] [-85057688713 139557891636] [621396377215 142456821408] [235311099488 53945714047] [1214292963837 360234473807] [ 461524670038 136916791591] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ 775402698292 940501859587] [ 988381946101 1198828763864] [ 7872797599680 14341022677663] [ 1374197311073 2503226401055] [178777460839951 226176323631666] [231813924404796 293274224514487] [-211539085964897 -124130073312081] [-274097154018824 -160838833484585] [218963293856347 310907254441867] [337173075119518 478754010368081] [24272804005834658 14219400333952293] [ 9021054286030389 5284679194729541] [27599084743679817 15562744500880357] [12478102382414936 7036230405351409] [32711801771534160 10118288575048201] [88457974646193719 27361480131410947] [ -687618373084674810577 -2587126872683566362302] [ -301735684600955117751 -1135264164883761283939] [ 96511 155701] [ 28275 45616] [26788114 8297697] [70220393 21750973] [ -28652104 -7763365] [-101781395 -27577944] [-1131333313 -669964123] [ -894820880 -529903857] [-59118636169 -20990309020] [-24753731334 -8788911649] [14972014473 34070749579] [ 6704536004 15257036229] [ 74928070698 21966449951] [253267910821 74249835014] [20853224792 4989575889] [47217450231 11297775455] [1214292963837 360234473807] [ 461524670038 136916791591] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ 775402698292 940501859587] [ 988381946101 1198828763864] [ 7872797599680 14341022677663] [ 1374197311073 2503226401055] [178777460839951 226176323631666] [231813924404796 293274224514487] [-211539085964897 -124130073312081] [-274097154018824 -160838833484585] [218963293856347 310907254441867] [337173075119518 478754010368081] [24272804005834658 14219400333952293] [ 9021054286030389 5284679194729541] [32711801771534160 10118288575048201] [88457974646193719 27361480131410947] [ -157969566299418866210 -1038718741292061163377] [ -69319054142844350577 -455802990117321124193] [ 96511 155701] [ 28275 45616] [ -28652104 -7763365] [-101781395 -27577944] [ 120929027 -198413576] [-170278202 279382939] [-18753416456 -11405800987] [-14831696205 -9020616356] [ 19791831799 -4315819386] [-35066512786 7646626003] [-14975211813 -4390281500] [-50618446399 -14839805377] [377888654221 600623181828] [208263657964 331018090933] [254009873356 90361069155] [106357190625 37835338171] [ 24091937426 86915826289] [ 85534088277 308578999979] [ 530064318909 1812879534839] [ 297199479112 1016455615341] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [ 3501321989573 -1570962722003] [-2243451109312 1006584961869] [ -345389284481 282192071278] [ 2338895725737 -1910938928927] [133760019715795 36184722421542] [226925540441902 61387832542903] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [955017288165885557 217614178145613918] [200139155232778487 45604533363351431] [-26380878693674228743 -62751699269476296356] [-15487752488971594035 -36840425136448262827] [-1 0] [14 -1] [ 1 0] [-15 1] [ 1 0] [-18 1] [ 1 0] [-20 1] [ 1 0] [-24 1] [ 1 24] [ 0 1] [ 1 0] [-28 1] [ 1 0] [-30 1] [-1 0] [33 -1] [ 1 0] [-38 1] [-1 0] [39 -1] [ 1 0] [-43 1] [-1 0] [47 -1] [ 1 0] [-52 1] [ -1 -53] [ 0 -1] [3070 2241] [5229 3817] [ 96511 155701] [ 28275 45616] [-10682725 6621216] [ 18470939 -11448397] [25337584 6854317] [32746603 8858603] [-344185829 -486421824] [-556996419 -787177133] [1617457841 1169831520] [2609624160 1887418961] [ 305829827 -1043859568] [ -415712460 1418911403] [1864786627 1134160551] [1468388122 893071549] [-823236115 180911672] [ 568877077 -125014563] [71345974183 49676152271] [39347313561 27396404104] [-14975211813 -4390281500] [-50618446399 -14839805377] [1990308790759 835587653774] [1220882300706 512560755355] [454850729337 172931662453] [209567227937 79676269126] [ 102302243147 -343228803095] [ -82872367120 278040661683] [-103876649931511 -39493392162362] [ -43494477680453 -16536386811317] [-365710291403131 -83314436526438] [-828076396543227 -188648555976217] [ 1 0] [-15 1] [ 1 24] [ 0 1] [ 1 0] [-24 1] [ 1 0] [-26 1] [ 1 0] [-28 1] [ 1 0] [-28 1] [ 1 0] [-36 1] [-1 0] [37 -1] [ -1 -38] [ 0 -1] [ -1 -46] [ 0 -1] [ 1 0] [-50 1] [ 1 52] [ 0 1] [ -1 -68] [ 0 -1] [ -1 -15] [ 0 -1] [ 229 552] [ 782 1885] [3070 5229] [2241 3817] [56815 33343] [33038 19389] [-245451 -435782] [-135145 -239941] [1689637 3010228] [2914288 5192045] [-1330541 -575653] [-4726492 -2044897] [ 244441 1028280] [ 135300 569161] [-32069005 -18987137] [-39422807 -23341112] [ 17957829 31089715] [ 61968995 107284594] [ 4929557 -17498216] [ -1350094 4792365] [133310510 81079261] [105325079 64058562] [-581167351 -477021650] [-477755387 -392141201] [213411686 949772345] [162761245 724356441] [-23533736982 -7013782793] [-30561537169 -9108284999] [72318384991 19847779821] [50940666635 13980665296] [33475753719 20272741675] [11910914285 7213187504] [ 96511 155701] [ 28275 45616] [26788114 8297697] [70220393 21750973] [-5348455197 -1213930346] [-7572213595 -1718653243] [ 74928070698 21966449951] [253267910821 74249835014] [ 49193342963 -80713681859] [-85057688713 139557891636] [621396377215 142456821408] [235311099488 53945714047] [1214292963837 360234473807] [ 461524670038 136916791591] [-4051736370019 -5147811105330] [-1678985648505 -2133184436929] [ 775402698292 940501859587] [ 988381946101 1198828763864] [-1755074437012 -474782304349] [-6232646191531 -1686053912360] [ -3460910580436 19715380804057] [ 11671658014015 -66488624023346] [-58595183347648 -15876426793153] [-46345487156095 -12557358676757] [ 431310044866315 1115316220023319] [ 114352252326016 295701255589667] [ 23326787766790319 -9021054286030389] [-16111432812040971 6230695433773880] [ 8881424487797552 14134588322904193] [10431677684974079 16601781594486024] [ 13276248937374599 -56197524898249505] [ -7790490380127124 32976654714139779] [-101860433172130441 -21346468541712346] [-161415045597039392 -33827081681201913] [333241942069324804176 260665976864065420049] [186844005630133325215 146151696711219215861] [ 96511 155701] [ 28275 45616] [ 48099 21125] [130975 57524] [-1279610 -4617057] [ -751277 -2710739] [-10413463 -3050058] [-13464396 -3943663] [-76944644 47722841] [ 32306607 -20037302] [ -91772048 -24826151] [-149841033 -40534958] [ 31838094 140718881] [ 19657813 86884141] [300755309 513565899] [486421824 830607653] [617133097 446294271] [957399459 692365870] [381073953 220395122] [616333147 356457895] [1599014243 5775792121] [ 988244661 3569634074] [ -789137174 -442472753] [-1272606037 -713555913] [-1098098487 -324155113] [ -676950755 -199833668] [-5058128033 1921246359] [ 3580154506 -1359862535] [877189890166 333455958161] [514672945415 195648356276] [130928843078 162434177711] [ 24140459053 29949364278] [ 975769909256 -1579082028541] [-2236866911555 3619907015751] [-40708470398952 -28665074567789] [-23994283976083 -16895695972719] [ -34657066394306 48975184724445] [ 90798769218339 -128311105291676] [ -14404658715913 49161894864880] [ 53249775245615 -181737027154377] [-116317346012735 -196112139769083] [ -71803437058893 -121061270456192] [ -1 -15] [ 0 -1] [1576 3735] [2241 5311] [-22297 18406] [ 27122 -22389] [ 27715959 -17012479] [-20058797 12312396] [38363388 93058409] [10701763 25959361] [ -264816057 -414134509] [ -690692996 -1080145245] [556066244 323727925] [206211031 120050929] [-158137091 -59780144] [-380592014 -143874187] [ 237647617 -644237979] [ -65203471 176759830] [9167753548 5036418921] [5403642431 2968557874] [ 6405132431 10931024867] [ 2450903781 4182722288] [-11882381283 -28989245657] [ -5337261832 -13021227875] [11632668010 2671489909] [27579183561 6333672595] [-30665905489 -43373448075] [-21273937519 -30089573734] [-11213047789 -19866127360] [ -4578944109 -8112503269] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [-2012498102784 -907356445297] [ -726042574703 -327344114663] [1509701020657 278358191256] [1861449280384 343213422865] [11730418483875328 6945307375718725] [51828052646181491 30686181981270942] [ 43601 27040] [113906 70641] [ 96511 155701] [ 28275 45616] [ 291924 768413] [ 418315 1101104] [ 2009879 -556439] [-5249881 1453440] [-15266875 -5823759] [ -6449861 -2460388] [-79126220 21804749] [128078371 -35294454] [ 380586231 -220887397] [-674842823 391670172] [ 586138185 2704392616] [ 354896129 1637461089] [ -29879674319 -102681121848] [ -13014673225 -44724759479] [ 520053646109 -1379445007821] [-1918291662687 5088278637092] [ 273311415679 1029580930499] [ 122645341710 462012553429] [ -36527906369244 -101608366495195] [ -14156540154929 -39378739800349] [12948464395820 4812338504949] [30851617570071 11466103055459] [ -32383137640735 -9493665617316] [-109459780751364 -32089989812815] [-486225731083327 -300074514861798] [-344591587587998 -212664914381515] [-26578263354164719 -10135379872403394] [-15739431524512185 -6002089577896189] [ 9451574317371690 -2616297187761821] [-16761494327295289 4639761482971983] [-2144239832315991533898 -7986294908222146637135] [-1140314056942620430801 -4247138873872448704832] [ 43601 -27040] [-113906 70641] [ 96511 155701] [ 28275 45616] [ -63737053 39411653] [ 168624332 -104268449] [-71210004 -27597293] [-51293995 -19878884] [ 12051214 -7763365] [-68579615 44178834] [-556034950 -676113499] [-391517001 -476067070] [ -30433450613 -11616452002] [-102869570742 -39265328345] [-15070821847 -6322975726] [-36479222748 -15304887967] [178157546774 69057145767] [255757513443 99136321793] [-117990474887 -43589849502] [ -73403077349 -27117689777] [ 78002559451 133196532209] [110803084626 189206440585] [229257918990 84118558183] [ 95001429983 34857610811] [377888654221 600623181828] [208263657964 331018090933] [-5730722018524 -1550273523735] [-1678985648505 -454198788424] [44953896290950 32515603276641] [20318981206639 14696922545368] [69072587312816914 89311331173618765] [24311360000949465 31434755940045259] [-146643861102541925 -207466122966560967] [-647169994582246947 -915591342636447230] [-1104397730030248909 -3939775977770246893] [ -403718066654482185 -1440204645072578734] [ 43601 -27040] [-113906 70641] [ 96511 155701] [ 28275 45616] [5297516 3285523] [1553057 963207] [-4083109 -5290207] [-2536149 -3285916] [-49187116 -14434027] [-21588101 -6335058] [-71210004 -27597293] [-51293995 -19878884] [ 79956995 210220979] [ 46357441 121881852] [315104849 95613003] [387214983 117493550] [-556034950 -676113499] [-391517001 -476067070] [ -851560564 -2074070445] [-2028911835 -4941640384] [-1064580009 -2592819983] [ -230837266 -562211831] [ 3454664279 9096036432] [ 8222614698 21649919303] [-1599581031700 -485304671831] [-4350348648729 -1319873442784] [11612855553209 3523716372240] [ 9550264886640 2897859582089] [1720451503540 4616214519207] [2224598757757 5968912848655] [-321480480103671 -520838236252477] [-227326018127399 -368296334189844] [-30633104095620964 -11747401020293181] [ -8974890168894675 -3441754828305634] [19371 10855] [15197 8516] [ 43601 -27040] [-113906 70641] [ 96511 155701] [ 28275 45616] [2084089 824564] [ 610597 241581] [1031780 222483] [1697693 366074] [-8461036 -3125035] [-5246409 -1937731] [-5399221 1479729] [ 7504792 -2056789] [282969795 165767866] [432409259 253311701] [460629385 739963036] [109261704 175519897] [-10971476834 -14927898491] [ -7727057963 -10513510501] [ -5534376130 -4551864449] [-13164719281 -10827601209] [-11295510184 -47760717835] [ -6917709509 -29250097299] [12738590810 17547286869] [23561324451 32455498832] [-459174590929 -125833584091] [-189457533600 -51919511569] [ 8938653932014 2643279929137] [10525704098397 3112591962385] [-566368739356397 -215115230901461] [-234697229154146 -89141481747031] [93543722924158 21290989801167] [66412621368023 15115823916499] [ 1 0] [-15 1] [-1 0] [27 -1] [ 1 0] [-28 1] [ 1 0] [-30 1] [ 1 0] [-31 1] [ 1 0] [-32 1] [ 1 35] [ 0 1] [ 1 36] [ 0 1] [-1 0] [36 -1] [ 1 0] [-36 1] [ 1 0] [-37 1]
--------------------------------------------------------------------------- GAPError Traceback (most recent call last) <ipython-input-11-84a7232411b4> in <module> 8 G=SL(Integer(2),Integers()); S=G([Integer(0),-Integer(1),Integer(1),Integer(0)]); T=G([Integer(1),Integer(1),Integer(0),Integer(1)]) 9 for i in range(Integer(2),len(H.relations())): ---> 10 print(H.relations()[i].subs(a=S,b=S*T),"\n") 11 break /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__mul__ (build/cythonized/sage/structure/element.c:12164)() 1511 cdef int cl = classify_elements(left, right) 1512 if HAVE_SAME_PARENT(cl): -> 1513 return (<Element>left)._mul_(right) 1514 if BOTH_ARE_ELEMENT(cl): 1515 return coercion_model.bin_op(left, right, mul) /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/groups/libgap_wrapper.pyx in sage.groups.libgap_wrapper.ElementLibGAP._mul_ (build/cythonized/sage/groups/libgap_wrapper.c:7092)() 628 """ 629 P = (<ElementLibGAP> left)._parent --> 630 return P.element_class(P, (<ElementLibGAP> left)._libgap * \ 631 (<ElementLibGAP> right)._libgap) 632 /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__mul__ (build/cythonized/sage/structure/element.c:12164)() 1511 cdef int cl = classify_elements(left, right) 1512 if HAVE_SAME_PARENT(cl): -> 1513 return (<Element>left)._mul_(right) 1514 if BOTH_ARE_ELEMENT(cl): 1515 return coercion_model.bin_op(left, right, mul) /ext/sage/sage-9.2/local/lib/python3.8/site-packages/sage/libs/gap/element.pyx in sage.libs.gap.element.GapElement._mul_ (build/cythonized/sage/libs/gap/element.c:10749)() 1063 try: 1064 sig_GAP_Enter() -> 1065 sig_on() 1066 result = PROD(self.value, (<GapElement>right).value) 1067 sig_off() GAPError: Error, no method found! Error, no 1st choice method found for CallFuncList' on 2 arguments 
In [ ]:

`