G := sub; involutions := [ [ G!(1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 47)(24, 49)(26, 53)(27, 55)(28, 57)(30, 61)(32, 65)(34, 69)(35, 71)(36, 73)(38, 77)(40, 81)(42, 85)(43, 87)(44, 89)(46, 93)(48, 97)(50, 101)(51, 103)(52, 105)(54, 109)(56, 113)(58, 117)(59, 119)(60, 121)(62, 125)(63, 127)(64, 129)(66, 107)(67, 134)(68, 115)(70, 139)(72, 143)(74, 147)(75, 98)(76, 150)(78, 154)(79, 156)(80, 112)(82, 161)(83, 100)(84, 164)(86, 168)(88, 170)(90, 174)(91, 176)(92, 178)(94, 126)(95, 182)(96, 184)(99, 189)(102, 194)(104, 198)(106, 202)(108, 205)(110, 209)(111, 211)(114, 216)(116, 219)(118, 223)(120, 225)(122, 229)(123, 231)(124, 233)(128, 239)(130, 242)(131, 244)(132, 246)(133, 248)(135, 252)(136, 254)(137, 256)(138, 258)(140, 262)(141, 264)(142, 251)(144, 269)(145, 241)(146, 272)(148, 276)(149, 277)(151, 281)(152, 283)(153, 285)(155, 263)(157, 291)(158, 293)(159, 295)(160, 297)(162, 301)(163, 303)(165, 307)(166, 309)(167, 311)(169, 315)(171, 299)(172, 320)(173, 305)(175, 325)(177, 329)(179, 292)(180, 334)(181, 336)(183, 340)(185, 343)(186, 345)(187, 347)(188, 349)(190, 353)(191, 355)(192, 357)(193, 359)(195, 363)(196, 365)(197, 352)(199, 370)(200, 342)(201, 373)(203, 377)(204, 378)(206, 382)(207, 384)(208, 386)(210, 364)(212, 392)(213, 394)(214, 396)(215, 398)(217, 402)(218, 404)(220, 408)(221, 410)(222, 412)(224, 416)(226, 400)(227, 421)(228, 406)(230, 426)(232, 430)(234, 393)(235, 435)(236, 437)(237, 439)(238, 441)(240, 445)(243, 450)(245, 424)(247, 457)(249, 461)(250, 463)(253, 468)(255, 472)(257, 474)(259, 368)(260, 479)(261, 481)(265, 417)(266, 488)(267, 360)(268, 413)(270, 436)(271, 423)(273, 498)(274, 500)(275, 502)(278, 492)(279, 509)(280, 496)(282, 514)(284, 427)(286, 487)(287, 522)(288, 524)(289, 526)(290, 528)(294, 534)(296, 425)(298, 538)(300, 541)(302, 544)(304, 547)(306, 550)(308, 554)(310, 556)(312, 369)(313, 561)(314, 563)(316, 366)(317, 567)(318, 569)(319, 571)(321, 575)(322, 372)(323, 346)(324, 397)(326, 385)(327, 582)(328, 574)(330, 586)(331, 565)(332, 589)(333, 591)(335, 371)(337, 581)(338, 599)(339, 601)(341, 605)(344, 610)(348, 617)(350, 621)(351, 623)(354, 628)(356, 632)(358, 634)(361, 639)(362, 641)(367, 648)(374, 658)(375, 660)(376, 662)(379, 652)(380, 669)(381, 656)(383, 674)(387, 647)(388, 682)(389, 684)(390, 686)(391, 688)(395, 694)(399, 698)(401, 701)(403, 704)(405, 707)(407, 710)(409, 714)(411, 716)(414, 721)(415, 723)(418, 727)(419, 729)(420, 731)(422, 735)(428, 742)(429, 734)(431, 746)(432, 725)(433, 749)(434, 751)(438, 741)(440, 654)(442, 759)(443, 683)(444, 760)(446, 715)(447, 631)(448, 763)(449, 709)(451, 765)(452, 767)(453, 762)(454, 672)(455, 718)(456, 770)(458, 773)(459, 732)(460, 679)(462, 766)(464, 776)(465, 777)(466, 779)(467, 630)(469, 783)(470, 627)(471, 607)(473, 786)(475, 782)(476, 787)(477, 637)(478, 789)(480, 792)(482, 681)(483, 793)(484, 794)(485, 796)(486, 719)(489, 798)(490, 650)(491, 728)(493, 802)(494, 600)(495, 804)(497, 807)(499, 808)(501, 809)(503, 738)(504, 812)(505, 814)(506, 815)(507, 817)(508, 819)(510, 822)(511, 769)(512, 614)(513, 780)(515, 774)(516, 827)(517, 821)(518, 828)(519, 620)(520, 747)(521, 642)(523, 603)(525, 826)(527, 832)(529, 706)(530, 733)(531, 691)(532, 833)(533, 696)(535, 818)(536, 693)(537, 836)(539, 838)(540, 839)(542, 788)(543, 755)(545, 835)(546, 689)(548, 825)(549, 609)(551, 768)(552, 845)(553, 846)(555, 606)(557, 842)(558, 615)(559, 646)(560, 850)(562, 851)(564, 820)(566, 852)(568, 651)(570, 799)(572, 619)(573, 690)(576, 857)(577, 785)(578, 663)(579, 790)(580, 805)(583, 847)(584, 859)(585, 795)(587, 680)(588, 849)(590, 829)(592, 860)(593, 775)(594, 862)(595, 703)(596, 764)(597, 781)(598, 771)(602, 864)(604, 865)(608, 868)(611, 870)(612, 872)(613, 867)(616, 875)(618, 878)(622, 871)(624, 881)(625, 882)(626, 884)(629, 888)(633, 891)(635, 887)(636, 892)(638, 894)(640, 897)(643, 898)(644, 899)(645, 901)(649, 903)(653, 907)(655, 909)(657, 912)(659, 913)(661, 914)(664, 917)(665, 919)(666, 920)(667, 922)(668, 924)(670, 927)(671, 874)(673, 885)(675, 879)(676, 932)(677, 926)(678, 933)(685, 931)(687, 937)(692, 938)(695, 923)(697, 941)(699, 943)(700, 944)(702, 893)(705, 940)(708, 930)(711, 873)(712, 950)(713, 951)(717, 947)(720, 955)(722, 956)(724, 925)(726, 957)(730, 904)(736, 962)(737, 890)(739, 895)(740, 910)(743, 952)(744, 964)(745, 900)(748, 954)(750, 934)(752, 965)(753, 880)(754, 967)(756, 869)(757, 886)(758, 876)(761, 971)(772, 975)(778, 961)(784, 977)(791, 939)(797, 981)(800, 905)(801, 945)(803, 983)(806, 969)(810, 973)(811, 953)(813, 960)(816, 963)(823, 928)(824, 976)(830, 966)(831, 948)(834, 896)(837, 986)(840, 906)(841, 974)(843, 936)(844, 972)(848, 916)(853, 978)(854, 970)(855, 918)(856, 883)(858, 921)(861, 935)(863, 985)(866, 990)(877, 994)(889, 996)(902, 1000)(908, 1002)(911, 988)(915, 992)(929, 995)(942, 1005)(946, 993)(949, 991)(958, 997)(959, 989)(968, 1004)(979, 1006)(980, 1001)(982, 999)(984, 1007)(987, 998)(1003, 1008), G!(1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 18)(9, 19)(11, 23)(12, 26)(13, 27)(16, 34)(17, 35)(20, 42)(21, 43)(22, 46)(24, 50)(25, 51)(28, 58)(29, 59)(30, 62)(31, 63)(32, 66)(33, 67)(36, 74)(37, 75)(38, 78)(39, 79)(40, 82)(41, 83)(44, 90)(45, 91)(47, 95)(48, 98)(49, 99)(52, 106)(53, 107)(54, 110)(55, 111)(56, 114)(57, 115)(60, 122)(61, 123)(64, 130)(65, 131)(68, 136)(69, 137)(70, 140)(71, 141)(72, 144)(73, 145)(76, 151)(77, 152)(80, 158)(81, 159)(84, 165)(85, 166)(86, 153)(87, 128)(88, 171)(89, 172)(92, 148)(93, 179)(94, 181)(96, 185)(97, 186)(100, 191)(101, 192)(102, 195)(103, 196)(104, 199)(105, 200)(108, 206)(109, 207)(112, 213)(113, 214)(116, 220)(117, 221)(118, 208)(119, 183)(120, 226)(121, 227)(124, 203)(125, 234)(126, 236)(127, 237)(129, 240)(132, 247)(133, 249)(134, 250)(135, 253)(138, 259)(139, 260)(142, 266)(143, 267)(146, 273)(147, 274)(149, 278)(150, 279)(154, 286)(155, 288)(156, 289)(157, 292)(160, 298)(161, 299)(162, 302)(163, 304)(164, 305)(167, 312)(168, 313)(169, 316)(170, 317)(173, 322)(174, 323)(175, 326)(176, 327)(177, 330)(178, 331)(180, 335)(182, 338)(184, 341)(187, 348)(188, 350)(189, 351)(190, 354)(193, 360)(194, 361)(197, 367)(198, 368)(201, 374)(202, 375)(204, 379)(205, 380)(209, 387)(210, 389)(211, 390)(212, 393)(215, 399)(216, 400)(217, 403)(218, 405)(219, 406)(222, 413)(223, 414)(224, 417)(225, 418)(228, 423)(229, 424)(230, 427)(231, 428)(232, 431)(233, 432)(235, 436)(238, 442)(239, 443)(241, 447)(242, 448)(243, 451)(244, 452)(245, 454)(246, 455)(248, 459)(251, 465)(252, 466)(254, 470)(255, 460)(256, 440)(257, 475)(258, 476)(261, 458)(262, 482)(263, 484)(264, 485)(265, 487)(268, 491)(269, 492)(270, 494)(271, 495)(272, 496)(275, 503)(276, 504)(277, 506)(280, 511)(281, 512)(282, 515)(283, 516)(284, 518)(285, 519)(287, 523)(290, 529)(291, 473)(293, 532)(294, 535)(295, 449)(296, 513)(297, 471)(300, 542)(301, 483)(303, 477)(306, 551)(307, 552)(308, 543)(309, 527)(310, 557)(311, 558)(314, 539)(315, 564)(318, 570)(319, 572)(320, 573)(321, 576)(324, 490)(325, 579)(328, 584)(329, 478)(332, 590)(333, 592)(334, 593)(336, 596)(337, 598)(339, 602)(340, 603)(342, 607)(343, 608)(344, 611)(345, 612)(346, 614)(347, 615)(349, 619)(352, 625)(353, 626)(355, 630)(356, 620)(357, 600)(358, 635)(359, 636)(362, 618)(363, 642)(364, 644)(365, 645)(366, 647)(369, 651)(370, 652)(371, 654)(372, 655)(373, 656)(376, 663)(377, 664)(378, 666)(381, 671)(382, 672)(383, 675)(384, 676)(385, 678)(386, 679)(388, 683)(391, 689)(392, 633)(394, 692)(395, 695)(396, 609)(397, 673)(398, 631)(401, 702)(402, 643)(404, 637)(407, 711)(408, 712)(409, 703)(410, 687)(411, 717)(412, 718)(415, 699)(416, 724)(419, 730)(420, 732)(421, 733)(422, 736)(425, 650)(426, 739)(429, 744)(430, 638)(433, 750)(434, 752)(435, 753)(437, 756)(438, 758)(439, 599)(441, 629)(444, 761)(445, 723)(446, 606)(450, 640)(453, 768)(456, 771)(457, 701)(461, 691)(462, 727)(463, 775)(464, 681)(467, 781)(468, 782)(469, 601)(472, 785)(474, 684)(479, 790)(480, 610)(481, 748)(486, 710)(488, 657)(489, 799)(493, 735)(497, 648)(498, 685)(499, 755)(500, 797)(501, 677)(502, 705)(505, 800)(507, 818)(508, 820)(509, 690)(510, 823)(514, 742)(517, 661)(520, 680)(521, 624)(522, 686)(524, 634)(525, 658)(526, 682)(528, 725)(530, 669)(531, 621)(533, 789)(534, 834)(536, 792)(537, 826)(538, 837)(540, 840)(541, 617)(544, 763)(545, 662)(546, 841)(547, 842)(548, 843)(549, 844)(550, 646)(553, 795)(554, 721)(555, 847)(556, 716)(559, 849)(560, 741)(561, 714)(562, 754)(563, 605)(565, 688)(566, 815)(567, 622)(568, 853)(569, 854)(571, 731)(574, 856)(575, 653)(577, 808)(578, 858)(580, 855)(581, 720)(582, 674)(583, 764)(585, 811)(586, 860)(587, 861)(588, 641)(589, 862)(591, 765)(594, 722)(595, 659)(597, 863)(604, 866)(613, 873)(616, 876)(623, 880)(627, 886)(628, 887)(632, 890)(639, 895)(649, 904)(660, 902)(665, 905)(667, 923)(668, 925)(670, 928)(693, 894)(694, 939)(696, 897)(697, 931)(698, 942)(700, 945)(704, 868)(706, 946)(707, 947)(708, 948)(709, 949)(713, 900)(715, 952)(719, 954)(726, 920)(728, 958)(729, 959)(734, 961)(737, 913)(738, 963)(740, 960)(743, 869)(745, 916)(746, 965)(747, 966)(749, 967)(751, 870)(757, 968)(759, 864)(760, 940)(762, 910)(766, 972)(767, 901)(769, 883)(770, 922)(772, 976)(773, 918)(774, 891)(776, 933)(777, 956)(778, 874)(779, 969)(780, 906)(783, 919)(784, 950)(786, 879)(787, 957)(788, 978)(791, 979)(793, 943)(794, 911)(796, 872)(798, 982)(801, 885)(802, 971)(803, 975)(804, 926)(805, 867)(806, 899)(807, 973)(809, 977)(810, 934)(812, 930)(813, 878)(814, 888)(816, 962)(817, 875)(819, 932)(821, 909)(822, 929)(824, 927)(825, 917)(827, 924)(828, 881)(829, 915)(830, 938)(831, 974)(832, 985)(833, 935)(835, 865)(836, 964)(838, 898)(839, 944)(845, 889)(846, 970)(848, 984)(850, 987)(851, 882)(852, 892)(857, 921)(859, 941)(871, 991)(877, 995)(884, 988)(893, 997)(896, 998)(903, 1001)(907, 990)(908, 994)(912, 992)(914, 996)(936, 993)(937, 1004)(951, 989)(953, 1003)(955, 1006)(980, 1007)(981, 1005)(983, 1002)(986, 1000)(999, 1008), G!(1, 4)(2, 6)(3, 8)(5, 12)(7, 16)(9, 20)(10, 22)(11, 24)(13, 28)(14, 30)(15, 32)(17, 36)(18, 38)(19, 40)(21, 44)(23, 48)(25, 52)(26, 54)(27, 56)(29, 60)(31, 64)(33, 68)(34, 70)(35, 72)(37, 76)(39, 80)(41, 84)(42, 86)(43, 88)(45, 92)(46, 94)(47, 96)(49, 100)(50, 102)(51, 104)(53, 108)(55, 112)(57, 116)(58, 118)(59, 120)(61, 124)(62, 126)(63, 128)(65, 132)(66, 133)(67, 135)(69, 138)(71, 142)(73, 146)(74, 148)(75, 149)(77, 153)(78, 155)(79, 157)(81, 160)(82, 162)(83, 163)(85, 167)(87, 169)(89, 173)(90, 175)(91, 177)(93, 180)(95, 183)(97, 187)(98, 188)(99, 190)(101, 193)(103, 197)(105, 201)(106, 203)(107, 204)(109, 208)(110, 210)(111, 212)(113, 215)(114, 217)(115, 218)(117, 222)(119, 224)(121, 228)(122, 230)(123, 232)(125, 235)(127, 238)(129, 241)(130, 243)(131, 245)(134, 251)(136, 255)(137, 257)(139, 261)(140, 263)(141, 265)(143, 268)(144, 270)(145, 271)(147, 275)(150, 280)(151, 282)(152, 284)(154, 287)(156, 290)(158, 294)(159, 296)(161, 300)(164, 306)(165, 308)(166, 310)(168, 314)(170, 318)(171, 319)(172, 321)(174, 324)(176, 328)(178, 332)(179, 333)(181, 337)(182, 339)(184, 342)(185, 344)(186, 346)(189, 352)(191, 356)(192, 358)(194, 362)(195, 364)(196, 366)(198, 369)(199, 371)(200, 372)(202, 376)(205, 381)(206, 383)(207, 385)(209, 388)(211, 391)(213, 395)(214, 397)(216, 401)(219, 407)(220, 409)(221, 411)(223, 415)(225, 419)(226, 420)(227, 422)(229, 425)(231, 429)(233, 433)(234, 434)(236, 438)(237, 440)(239, 444)(240, 446)(242, 449)(244, 453)(246, 456)(247, 458)(248, 460)(249, 462)(250, 464)(252, 467)(253, 469)(254, 471)(256, 473)(258, 477)(259, 478)(260, 480)(262, 483)(264, 486)(266, 489)(267, 490)(269, 493)(272, 497)(273, 499)(274, 501)(276, 505)(277, 507)(278, 508)(279, 510)(281, 513)(283, 517)(285, 520)(286, 521)(288, 525)(289, 527)(291, 530)(292, 531)(293, 533)(295, 536)(297, 537)(298, 539)(299, 540)(301, 543)(302, 545)(303, 546)(304, 548)(305, 549)(307, 553)(309, 555)(311, 559)(312, 560)(313, 562)(315, 565)(316, 566)(317, 568)(320, 574)(322, 577)(323, 578)(325, 580)(326, 581)(327, 583)(329, 585)(330, 587)(331, 588)(334, 594)(335, 595)(336, 597)(338, 600)(340, 604)(341, 606)(343, 609)(345, 613)(347, 616)(348, 618)(349, 620)(350, 622)(351, 624)(353, 627)(354, 629)(355, 631)(357, 633)(359, 637)(360, 638)(361, 640)(363, 643)(365, 646)(367, 649)(368, 650)(370, 653)(373, 657)(374, 659)(375, 661)(377, 665)(378, 667)(379, 668)(380, 670)(382, 673)(384, 677)(386, 680)(387, 681)(389, 685)(390, 687)(392, 690)(393, 691)(394, 693)(396, 696)(398, 697)(399, 699)(400, 700)(402, 703)(403, 705)(404, 706)(405, 708)(406, 709)(408, 713)(410, 715)(412, 719)(413, 720)(414, 722)(416, 725)(417, 726)(418, 728)(421, 734)(423, 737)(424, 738)(426, 740)(427, 741)(428, 743)(430, 745)(431, 747)(432, 748)(435, 754)(436, 755)(437, 757)(439, 704)(441, 718)(442, 746)(443, 614)(445, 762)(447, 688)(448, 764)(450, 749)(451, 766)(452, 621)(454, 603)(455, 769)(457, 772)(459, 774)(461, 612)(463, 632)(465, 778)(466, 780)(468, 660)(470, 784)(472, 623)(474, 729)(475, 676)(476, 788)(479, 791)(481, 641)(482, 751)(484, 795)(485, 797)(487, 647)(488, 739)(491, 800)(492, 801)(494, 803)(495, 805)(496, 806)(498, 758)(500, 628)(502, 810)(503, 811)(504, 813)(506, 816)(509, 821)(511, 721)(512, 824)(514, 825)(515, 826)(516, 635)(518, 829)(519, 750)(522, 830)(523, 831)(524, 698)(526, 735)(528, 607)(529, 807)(532, 770)(534, 804)(535, 835)(538, 684)(541, 744)(542, 796)(544, 599)(547, 798)(550, 710)(551, 742)(552, 727)(554, 819)(556, 848)(557, 732)(558, 601)(561, 671)(563, 752)(564, 724)(567, 712)(569, 634)(570, 855)(571, 808)(572, 717)(573, 776)(575, 686)(576, 736)(579, 648)(582, 711)(584, 701)(586, 602)(589, 610)(590, 679)(591, 642)(592, 723)(593, 822)(596, 817)(598, 658)(605, 867)(608, 869)(611, 871)(615, 874)(617, 877)(619, 879)(625, 883)(626, 885)(630, 889)(636, 893)(639, 896)(644, 900)(645, 902)(651, 905)(652, 906)(654, 908)(655, 910)(656, 911)(662, 915)(663, 916)(664, 918)(666, 921)(669, 926)(672, 929)(674, 930)(675, 931)(678, 934)(682, 935)(683, 936)(689, 912)(692, 875)(694, 909)(695, 940)(702, 901)(707, 903)(714, 924)(716, 953)(730, 960)(731, 913)(733, 881)(753, 927)(756, 922)(759, 969)(760, 970)(761, 967)(763, 933)(765, 919)(767, 973)(768, 951)(771, 974)(773, 898)(775, 886)(777, 894)(779, 895)(781, 880)(782, 944)(783, 948)(785, 938)(786, 954)(787, 939)(789, 882)(790, 884)(792, 980)(793, 878)(794, 937)(799, 983)(802, 979)(809, 984)(812, 923)(814, 870)(815, 947)(818, 917)(820, 950)(823, 978)(827, 946)(828, 868)(832, 899)(833, 890)(834, 892)(836, 941)(837, 968)(838, 963)(839, 887)(840, 952)(841, 932)(842, 920)(843, 888)(844, 981)(845, 925)(846, 873)(847, 945)(849, 891)(850, 977)(851, 959)(852, 965)(853, 985)(854, 956)(856, 961)(857, 986)(858, 943)(859, 987)(860, 957)(861, 975)(862, 866)(863, 942)(864, 988)(865, 989)(872, 992)(876, 993)(897, 999)(904, 1002)(907, 998)(914, 1003)(928, 997)(949, 1000)(955, 996)(958, 1004)(962, 1005)(964, 1006)(966, 994)(971, 990)(972, 1001)(976, 1007)(982, 991)(995, 1008) ] ]; geometries := [* *]; for i in [1..#involutions] do G1 := sub; G2 := sub; G3 := sub; Append(~geometries,CosetGeometry(G,{G1,G2,G3})); end for;