G := sub<Sym(120)|(1, 9)(2, 23)(3, 102)(4, 85)(5, 70)(6, 60)(7, 100)(8, 16)(10, 48)(11, 75)(12, 17)(13, 27)(14, 91)(15, 110)(18, 79)(19, 78)(20, 32)(21, 61)(22,103)(24, 113)(25, 54)(26, 112)(28, 58)(29, 44)(30, 40)(31, 52)(33, 114)(34, 108)(35, 109)(36, 39)(37, 90)(38, 89)(41, 120)(42, 84)(43, 51)(45, 74)(46, 82)(47, 105)(49, 65)(50, 63)(53, 92)(55, 64)(56, 71)(57,69)(59, 97)(62, 101)(66, 115)(67, 119)(68, 95)(72, 73)(76, 80)(77, 111)(81, 107)(83, 104)(86, 99)(87, 88)(93, 96)(94, 98)(106, 116)(117, 118),(1, 43)(2, 21)(3, 64)(4, 65)(5, 34)(6, 95)(7, 41)(8, 36)(9, 98)(10, 114)(11,15)(12, 113)(13, 63)(14, 19)(16, 66)(17, 107)(18, 22)(20, 99)(23, 47)(24, 81)(25, 77)(26, 32)(27, 90)(28, 56)(29, 108)(30, 72)(31, 57)(33,53)(35, 75)(37, 92)(38, 101)(39, 115)(40, 73)(42, 45)(44, 46)(48, 50)(49, 102)(51, 94)(52, 85)(54, 119)(55, 69)(58, 96)(59, 97)(60, 76)(61, 68)(62, 82)(67, 111)(70, 89)(71, 112)(74, 79)(78, 110)(80, 105)(83, 117)(84, 118)(86, 93)(87, 100)(88, 120)(91, 106)(103, 104)(109,116),(1, 4)(2, 47)(7, 54)(8, 28)(9, 66)(10, 32)(11, 84)(12, 41)(14, 88)(15, 77)(17, 111)(18, 34)(22, 104)(23, 92)(24, 27)(26, 94)(30, 45)(31, 68)(39, 40)(42, 50)(44, 100)(46, 99)(48, 81)(49, 119)(51, 82)(52, 67)(56, 70)(57, 75)(58, 90)(60, 91)(62, 76)(63, 98)(65, 93)(69, 112)(71,97)(72, 96)(73, 95)(78, 108)(80, 110)(83, 102)(101, 120)(106, 114)(109, 113)(116, 117)>;

involutions :=

[
[
    G!(1, 9)(2, 23)(3, 102)(4, 85)(5, 70)(6, 60)(7, 100)(8, 16)(10, 48)(11, 
        75)(12, 17)(13, 27)(14, 91)(15, 110)(18, 79)(19, 78)(20, 32)(21, 61)(22,
        103)(24, 113)(25, 54)(26, 112)(28, 58)(29, 44)(30, 40)(31, 52)(33, 
        114)(34, 108)(35, 109)(36, 39)(37, 90)(38, 89)(41, 120)(42, 84)(43, 
        51)(45, 74)(46, 82)(47, 105)(49, 65)(50, 63)(53, 92)(55, 64)(56, 71)(57,
        69)(59, 97)(62, 101)(66, 115)(67, 119)(68, 95)(72, 73)(76, 80)(77, 
        111)(81, 107)(83, 104)(86, 99)(87, 88)(93, 96)(94, 98)(106, 116)(117, 
        118),
    G!(1, 43)(2, 21)(3, 64)(4, 65)(5, 34)(6, 95)(7, 41)(8, 36)(9, 98)(10, 114)(11,
        15)(12, 113)(13, 63)(14, 19)(16, 66)(17, 107)(18, 22)(20, 99)(23, 
        47)(24, 81)(25, 77)(26, 32)(27, 90)(28, 56)(29, 108)(30, 72)(31, 57)(33,
        53)(35, 75)(37, 92)(38, 101)(39, 115)(40, 73)(42, 45)(44, 46)(48, 
        50)(49, 102)(51, 94)(52, 85)(54, 119)(55, 69)(58, 96)(59, 97)(60, 
        76)(61, 68)(62, 82)(67, 111)(70, 89)(71, 112)(74, 79)(78, 110)(80, 
        105)(83, 117)(84, 118)(86, 93)(87, 100)(88, 120)(91, 106)(103, 104)(109,
        116),
    G!(1, 4)(2, 47)(7, 54)(8, 28)(9, 66)(10, 32)(11, 84)(12, 41)(14, 88)(15, 
        77)(17, 111)(18, 34)(22, 104)(23, 92)(24, 27)(26, 94)(30, 45)(31, 
        68)(39, 40)(42, 50)(44, 100)(46, 99)(48, 81)(49, 119)(51, 82)(52, 
        67)(56, 70)(57, 75)(58, 90)(60, 91)(62, 76)(63, 98)(65, 93)(69, 112)(71,
        97)(72, 96)(73, 95)(78, 108)(80, 110)(83, 102)(101, 120)(106, 114)(109, 
        113)(116, 117)
]
,
[
    G!(1, 37)(2, 35)(3, 4)(5, 95)(6, 27)(7, 71)(8, 118)(9, 90)(10, 87)(11, 75)(12,
        97)(13, 60)(14, 92)(15, 25)(16, 117)(17, 59)(18, 51)(19, 74)(20, 47)(21,
        77)(22, 58)(23, 109)(24, 107)(26, 112)(28, 103)(29, 96)(30, 69)(31, 
        65)(32, 105)(33, 83)(34, 98)(36, 86)(38, 89)(39, 99)(40, 57)(41, 80)(42,
        82)(43, 79)(44, 93)(45, 78)(46, 84)(48, 88)(49, 52)(50, 63)(53, 91)(54, 
        110)(55, 72)(56, 100)(61, 111)(62, 119)(64, 73)(66, 106)(67, 101)(68, 
        70)(76, 120)(81, 113)(85, 102)(94, 108)(104, 114)(115, 116),
    G!(1, 68)(2, 75)(3, 62)(4, 23)(5, 7)(6, 110)(8, 36)(9, 57)(10, 73)(11, 87)(12,
        48)(13, 37)(14, 55)(15, 100)(16, 86)(17, 18)(19, 69)(20, 112)(21, 
        35)(22, 107)(24, 67)(25, 45)(26, 32)(27, 83)(28, 115)(29, 51)(30, 
        74)(31, 98)(33, 54)(34, 41)(38, 49)(39, 56)(40, 114)(42, 77)(43, 61)(44,
        109)(46, 116)(47, 65)(50, 113)(52, 120)(53, 119)(58, 97)(59, 96)(60, 
        70)(63, 92)(64, 82)(66, 93)(71, 99)(72, 79)(76, 89)(78, 95)(80, 105)(81,
        111)(84, 103)(85, 88)(90, 117)(91, 106)(94, 108)(101, 102)(104, 118),
    G!(1, 44)(2, 65)(3, 36)(4, 100)(6, 74)(7, 9)(8, 81)(11, 60)(12, 78)(13, 
        118)(15, 113)(17, 114)(18, 116)(19, 61)(21, 33)(22, 69)(24, 101)(25, 
        55)(27, 120)(28, 48)(29, 85)(30, 95)(34, 117)(35, 79)(38, 64)(41, 
        108)(45, 73)(47, 93)(51, 97)(52, 98)(53, 87)(54, 66)(57, 96)(62, 80)(63,
        67)(71, 82)(72, 75)(76, 110)(77, 109)(84, 91)(89, 115)(103, 105)(104, 
        112)(106, 111)
]
,
[
    G!(1, 63)(2, 92)(3, 41)(4, 118)(5, 24)(6, 46)(8, 119)(9, 33)(10, 78)(11, 
        53)(12, 99)(13, 52)(14, 38)(15, 23)(16, 42)(17, 116)(18, 64)(19, 98)(20,
        107)(21, 54)(25, 74)(26, 105)(27, 113)(28, 56)(29, 36)(30, 70)(31, 
        120)(32, 85)(34, 81)(35, 72)(37, 69)(39, 71)(40, 111)(43, 104)(45, 
        76)(47, 101)(48, 115)(49, 106)(51, 87)(55, 108)(57, 79)(58, 95)(59, 
        109)(60, 89)(61, 100)(62, 114)(65, 77)(66, 75)(68, 93)(73, 117)(80, 
        103)(82, 110)(84, 88)(86, 102)(90, 97)(91, 94),
    G!(1, 30)(2, 119)(3, 22)(4, 100)(6, 67)(7, 64)(8, 108)(9, 72)(10, 86)(11, 
        29)(12, 79)(13, 114)(14, 89)(15, 116)(16, 62)(17, 118)(19, 81)(21, 
        28)(23, 104)(25, 94)(26, 88)(27, 59)(31, 42)(32, 80)(33, 97)(34, 
        101)(35, 78)(36, 53)(37, 56)(38, 105)(39, 50)(40, 112)(41, 71)(43, 
        110)(44, 95)(45, 66)(47, 69)(48, 111)(49, 68)(51, 106)(52, 57)(54, 
        98)(55, 92)(60, 74)(61, 82)(63, 85)(65, 102)(70, 76)(73, 96)(75, 
        103)(77, 90)(83, 115)(84, 91)(87, 93)(99, 120)(107, 109),
    G!(1, 30)(2, 55)(3, 57)(4, 65)(5, 34)(6, 96)(7, 83)(8, 61)(9, 44)(10, 41)(11, 
        98)(12, 70)(13, 107)(14, 115)(16, 43)(17, 32)(18, 28)(20, 116)(21, 
        51)(22, 74)(23, 112)(24, 108)(25, 84)(26, 29)(27, 109)(31, 73)(35, 
        59)(36, 49)(37, 97)(38, 95)(39, 50)(40, 64)(42, 54)(45, 87)(47, 53)(52, 
        66)(56, 111)(60, 85)(62, 118)(63, 93)(67, 88)(68, 69)(72, 105)(75, 
        89)(76, 80)(77, 114)(78, 120)(79, 110)(81, 86)(82, 117)(90, 99)(91, 
        92)(94, 102)(100, 119)(103, 104)(106, 113)
]
,
[
    G!(1, 82)(2, 61)(3, 85)(4, 51)(5, 10)(6, 12)(7, 105)(8, 116)(11, 45)(13, 
        32)(14, 100)(15, 81)(16, 36)(17, 107)(18, 102)(20, 72)(21, 111)(22, 
        66)(23, 101)(24, 48)(25, 41)(26, 39)(27, 76)(28, 117)(29, 93)(30, 
        94)(31, 88)(33, 89)(34, 83)(35, 96)(37, 38)(40, 84)(42, 50)(43, 79)(44, 
        119)(47, 59)(49, 68)(52, 120)(53, 70)(54, 87)(55, 65)(56, 64)(57, 
        114)(58, 75)(60, 110)(62, 77)(63, 98)(67, 109)(69, 90)(71, 95)(73, 
        80)(74, 118)(78, 99)(91, 97)(92, 113)(106, 112),
    G!(1, 96)(2, 22)(3, 119)(4, 51)(5, 8)(6, 103)(7, 87)(9, 108)(10, 73)(11, 
        80)(12, 82)(13, 92)(14, 24)(15, 43)(16, 75)(17, 55)(18, 46)(19, 35)(20, 
        25)(21, 110)(23, 84)(26, 54)(28, 39)(29, 69)(30, 90)(31, 47)(32, 74)(33,
        50)(34, 68)(36, 52)(37, 114)(38, 65)(40, 63)(42, 60)(44, 78)(45, 
        112)(49, 86)(56, 99)(57, 109)(58, 105)(61, 85)(62, 83)(64, 79)(66, 
        81)(67, 101)(70, 76)(71, 89)(77, 115)(91, 117)(93, 95)(94, 111)(97, 
        120)(98, 107)(102, 104)(106, 113)(116, 118),
    G!(1, 80)(2, 38)(3, 55)(4, 110)(5, 105)(6, 69)(7, 99)(8, 24)(9, 54)(10, 
        66)(11, 31)(12, 74)(13, 115)(14, 76)(15, 28)(16, 47)(17, 93)(18, 67)(19,
        87)(20, 112)(21, 79)(23, 97)(25, 96)(26, 117)(27, 42)(30, 81)(32, 
        46)(33, 57)(34, 52)(35, 72)(36, 75)(37, 41)(39, 116)(40, 63)(43, 85)(44,
        49)(45, 68)(48, 84)(50, 77)(51, 82)(53, 56)(58, 118)(59, 114)(60, 
        120)(61, 70)(62, 119)(64, 106)(71, 92)(73, 109)(83, 102)(88, 100)(89, 
        90)(91, 95)(94, 98)(101, 113)(104, 108)
]
,
[
    G!(2, 47)(4, 86)(5, 13)(6, 31)(7, 91)(8, 50)(9, 78)(10, 113)(11, 114)(12, 
        119)(14, 49)(15, 96)(16, 116)(17, 93)(18, 103)(19, 102)(20, 81)(21, 
        67)(22, 46)(23, 107)(24, 77)(25, 44)(26, 90)(27, 72)(28, 118)(29, 
        71)(30, 106)(32, 120)(33, 36)(35, 76)(37, 74)(38, 98)(39, 45)(40, 
        58)(41, 88)(42, 89)(48, 100)(51, 115)(52, 92)(53, 59)(54, 73)(55, 
        110)(56, 70)(57, 69)(60, 109)(61, 64)(62, 68)(63, 117)(65, 111)(66, 
        108)(75, 112)(80, 97)(84, 94)(87, 105)(95, 101)(99, 104),
    G!(1, 38)(2, 5)(3, 89)(4, 67)(6, 52)(7, 73)(8, 71)(9, 21)(10, 87)(11, 60)(12, 
        103)(13, 97)(15, 115)(17, 108)(18, 93)(19, 61)(22, 119)(23, 58)(24, 
        31)(25, 70)(26, 65)(27, 90)(28, 118)(29, 106)(30, 48)(32, 56)(33, 
        72)(34, 94)(35, 91)(36, 109)(37, 88)(40, 59)(41, 114)(42, 83)(43, 
        69)(44, 105)(45, 75)(46, 101)(49, 80)(50, 53)(51, 95)(54, 81)(55, 
        102)(57, 82)(62, 86)(63, 100)(64, 78)(66, 96)(68, 99)(74, 111)(77, 
        113)(79, 84)(85, 98)(92, 120)(104, 110)(107, 117),
    G!(1, 17)(2, 118)(4, 43)(5, 110)(6, 75)(7, 109)(8, 88)(9, 21)(10, 60)(11, 
        100)(12, 77)(13, 71)(14, 72)(15, 63)(16, 27)(18, 85)(19, 73)(20, 30)(22,
        107)(23, 87)(24, 49)(25, 69)(26, 35)(28, 98)(29, 78)(31, 44)(33, 
        116)(34, 93)(36, 37)(38, 70)(39, 90)(40, 68)(41, 96)(42, 74)(45, 94)(46,
        55)(47, 50)(48, 112)(52, 104)(53, 76)(56, 117)(57, 62)(58, 114)(59, 
        61)(64, 81)(65, 103)(66, 92)(67, 105)(80, 108)(82, 113)(83, 91)(84, 
        106)(86, 111)(89, 119)(97, 99)(115, 120)
]
,
[
    G!(1, 76)(3, 108)(4, 82)(5, 14)(7, 88)(8, 95)(9, 61)(10, 37)(11, 46)(12, 
        45)(13, 114)(15, 55)(16, 105)(17, 83)(18, 54)(19, 109)(20, 52)(21, 
        36)(22, 42)(24, 74)(25, 117)(26, 28)(27, 90)(29, 57)(30, 53)(31, 62)(32,
        93)(33, 48)(34, 112)(35, 86)(38, 44)(39, 80)(40, 73)(41, 97)(43, 47)(49,
        69)(50, 72)(51, 68)(56, 78)(58, 102)(59, 120)(63, 92)(64, 70)(65, 
        89)(67, 79)(71, 99)(75, 106)(77, 111)(81, 107)(84, 103)(85, 116)(87, 
        100)(91, 110)(96, 101)(104, 113)(118, 119),
    G!(1, 107)(2, 37)(3, 120)(5, 93)(6, 14)(7, 10)(8, 24)(9, 71)(11, 33)(12, 
        49)(13, 51)(15, 53)(16, 63)(17, 105)(19, 115)(20, 100)(21, 32)(23, 
        46)(25, 118)(26, 76)(27, 70)(28, 57)(29, 34)(30, 75)(31, 56)(35, 90)(36,
        42)(38, 39)(40, 88)(41, 62)(43, 104)(44, 98)(45, 68)(47, 112)(48, 
        50)(52, 86)(54, 55)(58, 96)(59, 69)(60, 92)(61, 81)(64, 74)(66, 91)(72, 
        89)(73, 79)(77, 84)(80, 103)(82, 83)(85, 108)(87, 102)(94, 106)(95, 
        101)(97, 109)(99, 113)(114, 117)(116, 119),
    G!(1, 66)(2, 17)(3, 115)(4, 104)(5, 14)(6, 101)(7, 12)(8, 58)(9, 102)(10, 
        96)(13, 119)(15, 87)(16, 37)(18, 46)(19, 43)(20, 91)(21, 49)(22, 83)(23,
        48)(24, 105)(25, 113)(27, 29)(28, 114)(30, 39)(31, 80)(32, 47)(33, 
        118)(34, 78)(35, 95)(40, 45)(41, 65)(42, 69)(44, 110)(50, 75)(51, 
        108)(52, 76)(53, 109)(54, 70)(55, 77)(56, 93)(57, 98)(59, 60)(61, 
        73)(62, 92)(63, 112)(64, 120)(67, 81)(68, 97)(71, 100)(72, 111)(79, 
        86)(82, 99)(85, 103)(88, 107)(90, 116)(106, 117)
]
,
[
    G!(1, 43)(2, 35)(3, 62)(4, 9)(5, 53)(6, 78)(7, 119)(10, 73)(11, 27)(12, 
        120)(13, 63)(14, 107)(15, 90)(16, 93)(17, 19)(18, 69)(20, 84)(21, 
        75)(22, 55)(23, 57)(24, 38)(25, 109)(28, 39)(29, 60)(30, 96)(31, 47)(33,
        34)(37, 92)(40, 114)(41, 54)(42, 46)(44, 45)(48, 52)(49, 67)(50, 85)(51,
        70)(56, 115)(58, 72)(59, 74)(61, 68)(64, 82)(65, 98)(66, 86)(71, 
        104)(76, 108)(77, 116)(79, 97)(81, 101)(83, 87)(88, 113)(89, 94)(95, 
        110)(99, 118)(100, 117)(102, 111)(103, 112),
    G!(1, 100)(2, 93)(3, 87)(4, 44)(6, 64)(7, 75)(8, 82)(9, 72)(10, 90)(11, 
        30)(12, 17)(13, 19)(14, 40)(15, 24)(18, 62)(21, 79)(22, 112)(23, 68)(25,
        89)(26, 49)(27, 77)(28, 51)(29, 105)(31, 92)(32, 58)(33, 35)(34, 76)(36,
        53)(38, 74)(39, 88)(41, 111)(42, 83)(45, 84)(46, 70)(47, 65)(48, 97)(50,
        102)(52, 63)(54, 57)(55, 115)(56, 99)(60, 95)(61, 118)(66, 96)(67, 
        98)(69, 104)(71, 81)(73, 91)(78, 114)(80, 116)(85, 103)(94, 119)(101, 
        113)(106, 108)(109, 120)(110, 117),
    G!(1, 28)(2, 110)(3, 102)(4, 85)(5, 88)(6, 101)(7, 20)(8, 118)(9, 58)(10, 
        68)(12, 81)(13, 119)(14, 44)(15, 23)(16, 117)(17, 107)(18, 51)(19, 
        98)(21, 111)(22, 90)(24, 59)(25, 109)(27, 67)(29, 91)(30, 40)(31, 
        49)(32, 100)(33, 115)(34, 74)(35, 54)(36, 82)(37, 103)(39, 46)(41, 
        76)(42, 86)(43, 79)(45, 108)(47, 71)(48, 95)(52, 65)(53, 96)(55, 73)(56,
        105)(57, 69)(60, 62)(61, 77)(64, 72)(66, 114)(70, 87)(78, 94)(80, 
        120)(83, 116)(84, 99)(92, 93)(97, 113)(104, 106)
]
,
[
    G!(1, 73)(3, 8)(4, 117)(5, 13)(6, 68)(7, 56)(9, 55)(10, 109)(11, 69)(12, 
        33)(14, 19)(15, 54)(16, 85)(17, 42)(18, 43)(20, 23)(21, 45)(22, 29)(24, 
        37)(25, 100)(26, 30)(27, 60)(28, 41)(31, 46)(34, 72)(35, 67)(36, 
        111)(39, 80)(40, 75)(44, 78)(47, 119)(48, 105)(49, 82)(50, 89)(52, 
        104)(53, 99)(57, 112)(58, 61)(59, 114)(62, 87)(64, 108)(65, 83)(66, 
        92)(70, 95)(71, 110)(74, 120)(76, 106)(77, 116)(81, 90)(84, 97)(86, 
        96)(91, 103)(93, 115)(94, 107)(98, 113)(102, 118),
    G!(1, 26)(2, 7)(3, 63)(4, 5)(6, 79)(9, 85)(10, 40)(11, 57)(12, 39)(13, 62)(14,
        118)(15, 98)(16, 87)(17, 38)(19, 55)(20, 22)(21, 97)(23, 96)(24, 
        111)(27, 70)(28, 54)(29, 53)(30, 76)(31, 52)(32, 61)(33, 60)(34, 47)(35,
        41)(36, 80)(37, 64)(42, 107)(43, 91)(44, 116)(45, 71)(46, 67)(48, 
        89)(50, 94)(51, 90)(56, 74)(58, 65)(59, 75)(66, 120)(68, 106)(69, 
        103)(72, 108)(77, 102)(78, 117)(81, 109)(82, 92)(83, 115)(84, 104)(86, 
        88)(93, 100)(95, 119)(101, 112)(110, 113),
    G!(1, 25)(2, 24)(3, 34)(4, 89)(5, 86)(7, 66)(9, 54)(10, 72)(11, 65)(12, 
        113)(13, 62)(14, 49)(15, 112)(16, 103)(17, 60)(18, 87)(19, 116)(20, 
        85)(21, 117)(22, 84)(26, 40)(27, 69)(28, 48)(29, 37)(30, 93)(31, 82)(32,
        96)(33, 63)(35, 44)(36, 67)(38, 64)(39, 119)(41, 120)(42, 51)(45, 
        104)(46, 75)(47, 77)(50, 71)(52, 53)(55, 110)(56, 70)(57, 99)(58, 
        90)(59, 105)(61, 98)(68, 97)(73, 78)(76, 79)(80, 115)(88, 94)(91, 
        108)(92, 102)(95, 111)(100, 118)(101, 114)(106, 109)
]
,
[
    G!(1, 9)(2, 23)(3, 55)(4, 52)(5, 108)(6, 60)(7, 87)(8, 16)(10, 33)(11, 93)(12,
        24)(13, 90)(14, 26)(15, 28)(17, 113)(18, 117)(19, 56)(20, 106)(21, 
        61)(22, 42)(25, 119)(27, 37)(29, 38)(30, 73)(31, 85)(32, 116)(34, 
        70)(35, 99)(36, 39)(40, 72)(43, 51)(44, 89)(45, 83)(46, 62)(47, 105)(48,
        114)(49, 57)(50, 92)(53, 63)(54, 67)(58, 110)(64, 102)(65, 69)(66, 
        115)(68, 95)(71, 78)(74, 104)(75, 96)(76, 80)(79, 118)(82, 101)(84, 
        103)(86, 109)(88, 100)(91, 112)(94, 98),
    G!(1, 86)(2, 13)(3, 64)(5, 17)(6, 95)(7, 117)(8, 89)(9, 47)(10, 62)(11, 
        15)(12, 109)(14, 19)(16, 92)(18, 67)(20, 97)(21, 63)(22, 111)(23, 
        98)(24, 90)(25, 77)(26, 51)(27, 81)(29, 80)(30, 42)(32, 94)(33, 53)(34, 
        107)(35, 68)(36, 70)(37, 66)(38, 101)(39, 115)(40, 73)(41, 83)(43, 
        93)(44, 71)(45, 72)(46, 112)(48, 96)(49, 54)(50, 58)(52, 103)(55, 
        100)(59, 99)(60, 106)(61, 75)(69, 87)(74, 79)(76, 91)(82, 114)(84, 
        118)(85, 104)(88, 120)(102, 119)(105, 108)(113, 116),
    G!(1, 102)(2, 54)(3, 85)(4, 83)(5, 20)(6, 87)(7, 47)(8, 28)(9, 22)(10, 70)(11,
        94)(12, 111)(13, 35)(14, 60)(15, 120)(17, 41)(18, 34)(21, 61)(23, 
        44)(24, 109)(25, 105)(26, 84)(27, 113)(29, 53)(30, 39)(31, 67)(32, 
        56)(36, 74)(38, 89)(40, 45)(42, 63)(46, 99)(48, 97)(49, 95)(50, 98)(51, 
        82)(52, 68)(55, 64)(57, 112)(58, 90)(59, 107)(62, 80)(65, 96)(66, 
        104)(69, 75)(71, 81)(72, 93)(73, 119)(76, 110)(77, 101)(78, 108)(88, 
        91)(92, 100)(103, 115)(106, 114)(116, 117)
]
,
[
    G!(1, 23)(2, 82)(3, 96)(4, 22)(5, 19)(6, 14)(7, 79)(8, 39)(9, 101)(10, 33)(11,
        48)(12, 26)(13, 65)(15, 103)(16, 73)(17, 50)(18, 112)(20, 108)(24, 
        60)(25, 28)(27, 110)(29, 69)(30, 36)(31, 34)(32, 68)(35, 55)(37, 80)(38,
        90)(42, 51)(43, 52)(44, 91)(45, 114)(46, 77)(47, 87)(49, 116)(53, 
        94)(54, 92)(56, 106)(57, 95)(58, 76)(59, 115)(61, 111)(63, 71)(64, 
        81)(67, 113)(70, 88)(72, 97)(75, 99)(78, 98)(83, 93)(84, 119)(85, 
        100)(86, 120)(89, 117)(104, 107)(105, 118),
    G!(1, 4)(2, 70)(5, 78)(6, 90)(8, 27)(9, 87)(10, 103)(11, 62)(12, 55)(13, 
        105)(14, 98)(15, 52)(16, 41)(18, 95)(19, 58)(20, 115)(21, 118)(22, 
        46)(23, 50)(24, 67)(26, 109)(28, 77)(29, 38)(30, 83)(31, 60)(32, 35)(33,
        74)(34, 91)(36, 108)(37, 66)(39, 120)(40, 94)(42, 92)(43, 53)(44, 
        82)(45, 76)(47, 104)(48, 81)(49, 71)(51, 100)(54, 114)(56, 99)(61, 
        112)(63, 119)(64, 65)(68, 73)(69, 85)(72, 107)(75, 111)(79, 93)(80, 
        116)(84, 102)(88, 97)(89, 96)(101, 113)(110, 117),
    G!(1, 72)(2, 54)(3, 106)(4, 119)(5, 49)(6, 116)(7, 58)(8, 84)(9, 29)(10, 
        22)(11, 25)(12, 40)(13, 48)(14, 115)(16, 56)(17, 34)(18, 109)(19, 
        120)(20, 110)(21, 89)(23, 111)(24, 41)(26, 57)(27, 94)(28, 112)(30, 
        37)(31, 117)(33, 68)(35, 91)(36, 83)(38, 99)(42, 93)(43, 55)(44, 45)(46,
        61)(47, 78)(50, 60)(53, 70)(59, 85)(62, 65)(63, 102)(66, 79)(67, 87)(69,
        100)(71, 96)(73, 74)(75, 77)(76, 95)(80, 81)(82, 86)(88, 97)(90, 
        108)(92, 101)(98, 103)(105, 113)(107, 114)
]
,
[
    G!(1, 106)(2, 59)(3, 69)(4, 20)(5, 23)(6, 54)(7, 52)(8, 45)(9, 32)(10, 30)(11,
        24)(12, 48)(13, 34)(14, 33)(15, 31)(16, 81)(17, 117)(18, 99)(19, 84)(21,
        41)(25, 78)(26, 104)(27, 87)(28, 68)(35, 97)(37, 46)(38, 114)(39, 
        105)(42, 112)(43, 116)(44, 94)(47, 110)(49, 51)(50, 64)(53, 76)(55, 
        79)(56, 119)(57, 62)(58, 61)(60, 72)(63, 82)(65, 70)(66, 77)(67, 
        115)(71, 90)(73, 89)(74, 80)(75, 107)(83, 91)(85, 109)(86, 111)(88, 
        113)(92, 108)(93, 120)(98, 101)(103, 118),
    G!(1, 14)(2, 31)(3, 11)(5, 120)(6, 97)(7, 107)(8, 39)(9, 81)(10, 95)(12, 
        49)(13, 27)(15, 30)(16, 83)(17, 102)(18, 99)(19, 63)(20, 117)(21, 
        72)(22, 71)(23, 51)(24, 92)(25, 48)(26, 113)(28, 67)(29, 80)(32, 
        118)(33, 91)(34, 35)(36, 40)(37, 79)(38, 100)(41, 86)(43, 88)(44, 
        65)(45, 96)(46, 47)(50, 60)(52, 101)(54, 94)(55, 62)(56, 98)(57, 
        104)(58, 115)(59, 74)(61, 85)(64, 87)(68, 103)(69, 110)(70, 111)(75, 
        76)(77, 90)(78, 93)(82, 84)(89, 114)(106, 109)(108, 116),
    G!(1, 2)(3, 107)(4, 5)(6, 65)(7, 22)(8, 35)(9, 98)(10, 42)(11, 43)(12, 39)(13,
        96)(14, 21)(15, 18)(16, 61)(17, 20)(19, 41)(23, 34)(24, 40)(25, 50)(26, 
        29)(27, 57)(28, 54)(31, 95)(32, 108)(33, 63)(36, 117)(37, 76)(38, 
        53)(44, 74)(45, 69)(46, 66)(47, 90)(48, 68)(51, 84)(52, 87)(58, 71)(59, 
        113)(60, 111)(62, 104)(64, 73)(67, 70)(72, 119)(75, 105)(77, 79)(78, 
        100)(80, 88)(81, 109)(83, 106)(86, 112)(89, 118)(91, 120)(92, 94)(93, 
        101)(97, 115)(99, 116)(102, 103)
]
,
[
    G!(1, 41)(2, 11)(3, 32)(4, 23)(5, 7)(6, 15)(8, 40)(9, 116)(10, 67)(12, 55)(13,
        18)(14, 21)(17, 98)(19, 28)(20, 26)(22, 72)(24, 120)(25, 38)(27, 50)(29,
        42)(31, 99)(33, 107)(34, 49)(36, 115)(37, 93)(39, 91)(43, 71)(44, 
        52)(45, 97)(46, 74)(51, 54)(53, 111)(56, 89)(58, 92)(59, 80)(60, 
        110)(61, 66)(62, 112)(63, 68)(64, 83)(65, 81)(69, 118)(70, 100)(73, 
        96)(75, 88)(76, 82)(77, 78)(79, 95)(84, 86)(85, 87)(90, 103)(94, 
        104)(101, 102)(105, 109)(106, 113)(108, 114),
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        24)(11, 31)(12, 53)(13, 102)(14, 73)(15, 100)(16, 57)(17, 45)(18, 
        92)(20, 63)(21, 60)(22, 32)(23, 75)(25, 37)(26, 77)(27, 79)(28, 94)(29, 
        39)(30, 86)(33, 56)(34, 41)(36, 103)(38, 107)(40, 104)(42, 71)(43, 
        68)(44, 105)(46, 114)(48, 96)(49, 106)(51, 113)(52, 70)(58, 76)(59, 
        119)(64, 82)(65, 110)(66, 87)(72, 85)(74, 108)(78, 97)(80, 81)(83, 
        88)(89, 93)(90, 115)(91, 99)(95, 98)(101, 112),
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        101)(11, 32)(12, 22)(13, 73)(14, 67)(15, 36)(16, 108)(17, 20)(19, 
        60)(21, 27)(24, 25)(26, 52)(28, 33)(29, 69)(30, 75)(34, 80)(37, 112)(40,
        116)(42, 56)(44, 98)(45, 46)(47, 59)(48, 87)(49, 117)(50, 90)(53, 
        95)(54, 82)(55, 92)(57, 109)(58, 71)(61, 83)(62, 94)(64, 74)(65, 
        106)(66, 68)(70, 97)(72, 120)(76, 88)(77, 79)(78, 105)(81, 115)(84, 
        96)(85, 111)(86, 107)(89, 91)(99, 113)(102, 118)
]
,
[
    G!(1, 55)(2, 30)(3, 106)(4, 23)(5, 96)(6, 22)(7, 44)(8, 113)(9, 99)(10, 
        28)(11, 57)(12, 90)(13, 43)(14, 84)(15, 29)(16, 38)(17, 65)(19, 26)(20, 
        108)(21, 97)(24, 67)(25, 35)(27, 115)(31, 37)(32, 76)(33, 101)(34, 
        86)(36, 60)(39, 51)(40, 107)(42, 54)(46, 93)(47, 88)(48, 63)(50, 73)(52,
        56)(53, 116)(59, 109)(61, 98)(62, 120)(64, 95)(66, 111)(68, 117)(69, 
        82)(70, 83)(72, 79)(74, 81)(75, 119)(77, 102)(78, 118)(80, 112)(89, 
        104)(91, 100)(92, 103)(94, 110)(105, 114),
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        115)(11, 86)(12, 94)(13, 113)(15, 57)(16, 107)(17, 96)(18, 24)(19, 
        77)(20, 73)(21, 68)(22, 97)(23, 79)(25, 58)(26, 105)(27, 39)(28, 71)(29,
        34)(30, 51)(31, 49)(33, 106)(35, 78)(36, 99)(38, 61)(40, 92)(41, 75)(42,
        62)(43, 82)(44, 90)(46, 63)(48, 59)(52, 56)(54, 74)(64, 110)(66, 
        102)(69, 84)(70, 87)(72, 109)(76, 108)(80, 120)(81, 91)(83, 116)(85, 
        118)(88, 111)(93, 95)(101, 119)(114, 117),
    G!(1, 65)(2, 12)(4, 59)(5, 28)(6, 10)(7, 102)(8, 47)(9, 78)(11, 39)(13, 
        55)(14, 23)(15, 36)(16, 99)(17, 40)(18, 82)(20, 61)(21, 117)(22, 49)(24,
        46)(25, 30)(26, 51)(27, 119)(29, 50)(31, 101)(32, 84)(33, 97)(34, 
        45)(35, 83)(37, 88)(38, 118)(41, 42)(43, 120)(44, 75)(48, 73)(52, 
        74)(53, 111)(54, 93)(56, 63)(62, 90)(64, 94)(66, 71)(67, 108)(69, 
        86)(70, 72)(76, 115)(77, 110)(79, 100)(80, 92)(85, 106)(87, 98)(89, 
        104)(91, 114)(95, 103)(96, 116)(105, 107)(109, 112)
]
,
[
    G!(1, 20)(2, 101)(3, 68)(4, 118)(5, 117)(6, 71)(7, 54)(8, 76)(9, 40)(10, 
        108)(11, 30)(12, 73)(13, 86)(14, 49)(15, 111)(16, 74)(17, 27)(18, 
        64)(19, 81)(22, 104)(23, 33)(24, 99)(25, 61)(26, 66)(29, 98)(31, 
        105)(32, 78)(34, 36)(35, 38)(37, 53)(39, 65)(41, 91)(42, 100)(45, 
        88)(46, 77)(47, 109)(48, 107)(51, 67)(52, 110)(55, 85)(56, 112)(57, 
        113)(58, 60)(59, 92)(63, 115)(69, 70)(72, 106)(75, 120)(79, 116)(80, 
        83)(82, 102)(84, 119)(89, 97)(90, 95)(93, 94)(96, 114),
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        34)(12, 33)(13, 23)(14, 42)(15, 99)(17, 78)(19, 21)(20, 70)(22, 50)(25, 
        89)(26, 118)(27, 75)(28, 36)(29, 56)(30, 63)(31, 94)(35, 88)(37, 
        101)(38, 52)(39, 71)(40, 115)(43, 74)(44, 58)(45, 59)(46, 73)(47, 
        69)(48, 83)(49, 51)(53, 81)(54, 98)(55, 119)(57, 91)(60, 77)(61, 
        114)(62, 86)(65, 97)(66, 103)(68, 93)(79, 102)(80, 113)(82, 104)(84, 
        105)(85, 109)(87, 106)(90, 110)(100, 120)(111, 112),
    G!(1, 105)(2, 8)(3, 120)(4, 83)(5, 39)(6, 98)(7, 59)(10, 111)(11, 21)(12, 
        70)(13, 54)(14, 60)(15, 44)(17, 41)(18, 45)(20, 30)(22, 119)(23, 27)(24,
        89)(25, 87)(26, 82)(28, 84)(29, 64)(31, 108)(32, 56)(33, 43)(34, 47)(35,
        65)(36, 46)(37, 110)(38, 58)(40, 117)(42, 63)(48, 80)(50, 53)(51, 
        96)(52, 109)(55, 102)(57, 88)(61, 94)(62, 118)(66, 112)(67, 78)(68, 
        101)(72, 116)(73, 75)(74, 113)(77, 103)(79, 81)(85, 99)(86, 97)(90, 
        115)(91, 104)(92, 114)(93, 107)(100, 106)
]
,
[
    G!(1, 33)(2, 45)(3, 86)(4, 74)(5, 76)(6, 61)(7, 112)(8, 110)(9, 113)(10, 
        32)(11, 70)(12, 91)(13, 102)(14, 15)(16, 100)(17, 90)(18, 21)(19, 
        59)(20, 103)(22, 26)(23, 28)(24, 77)(25, 85)(27, 49)(29, 34)(30, 56)(31,
        107)(36, 81)(37, 48)(38, 51)(39, 46)(40, 104)(41, 73)(42, 117)(44, 
        89)(47, 84)(52, 71)(53, 79)(54, 69)(55, 68)(57, 114)(58, 111)(60, 
        96)(62, 87)(63, 80)(65, 93)(66, 120)(72, 95)(75, 106)(78, 101)(82, 
        118)(83, 105)(88, 119)(92, 98)(94, 99)(108, 109),
    G!(1, 37)(2, 91)(3, 12)(4, 105)(5, 33)(6, 96)(7, 15)(8, 23)(9, 40)(10, 65)(11,
        80)(13, 49)(14, 111)(16, 77)(17, 68)(18, 81)(19, 117)(20, 97)(21, 
        82)(22, 35)(24, 58)(25, 116)(26, 85)(27, 29)(30, 101)(31, 69)(32, 
        87)(34, 102)(36, 88)(38, 55)(39, 59)(41, 104)(42, 66)(43, 99)(44, 
        48)(45, 63)(47, 67)(50, 70)(51, 89)(52, 78)(53, 73)(54, 76)(56, 94)(57, 
        118)(60, 79)(62, 90)(64, 86)(71, 103)(74, 114)(75, 106)(83, 100)(93, 
        107)(95, 108)(98, 109)(110, 120)(112, 119),
    G!(1, 99)(2, 27)(3, 28)(4, 79)(5, 117)(6, 106)(7, 110)(8, 66)(9, 12)(10, 
        31)(11, 24)(13, 38)(14, 23)(15, 42)(16, 30)(17, 70)(18, 74)(19, 87)(20, 
        52)(21, 68)(22, 49)(25, 94)(26, 63)(32, 112)(34, 69)(35, 107)(36, 
        73)(37, 47)(40, 72)(41, 67)(43, 120)(44, 95)(45, 48)(46, 54)(50, 81)(51,
        56)(53, 96)(55, 80)(57, 60)(59, 115)(61, 82)(62, 90)(64, 77)(65, 
        102)(71, 101)(75, 103)(76, 118)(78, 109)(83, 105)(84, 114)(85, 88)(86, 
        108)(89, 104)(91, 119)(92, 100)(111, 116)
]
,
[
    G!(1, 28)(2, 96)(3, 72)(4, 8)(5, 6)(7, 38)(9, 107)(10, 17)(11, 23)(13, 25)(14,
        116)(15, 98)(16, 111)(18, 73)(19, 41)(20, 55)(21, 22)(24, 63)(26, 
        30)(27, 91)(29, 35)(31, 68)(32, 33)(34, 60)(36, 93)(37, 118)(39, 84)(40,
        67)(42, 51)(43, 70)(44, 100)(45, 92)(46, 112)(47, 103)(48, 62)(49, 
        120)(50, 82)(52, 94)(53, 106)(57, 78)(58, 66)(59, 69)(61, 75)(64, 
        90)(71, 97)(76, 81)(77, 95)(80, 110)(83, 113)(85, 115)(87, 99)(88, 
        109)(101, 102)(104, 114)(105, 108)(117, 119),
    G!(1, 49)(2, 53)(3, 31)(4, 90)(5, 71)(6, 13)(7, 43)(8, 22)(9, 85)(10, 107)(11,
        12)(14, 113)(15, 63)(16, 80)(17, 37)(18, 70)(19, 57)(20, 93)(21, 88)(23,
        86)(24, 35)(25, 100)(26, 34)(28, 120)(29, 46)(30, 36)(32, 66)(33, 
        116)(38, 60)(39, 55)(40, 91)(41, 62)(42, 67)(44, 117)(47, 114)(48, 
        73)(50, 79)(52, 59)(56, 95)(58, 101)(64, 109)(65, 75)(68, 110)(69, 
        77)(72, 111)(74, 87)(76, 84)(78, 81)(82, 105)(83, 103)(94, 108)(96, 
        115)(97, 102)(98, 112)(104, 119)(106, 118),
    G!(1, 51)(2, 92)(3, 50)(4, 37)(5, 119)(6, 96)(7, 48)(9, 94)(10, 105)(11, 
        26)(12, 110)(13, 88)(14, 81)(15, 100)(16, 74)(17, 31)(18, 83)(19, 
        116)(20, 113)(21, 65)(22, 39)(23, 91)(24, 55)(25, 72)(27, 68)(28, 
        86)(29, 77)(32, 87)(33, 102)(34, 38)(35, 120)(36, 118)(41, 71)(42, 
        98)(43, 79)(44, 111)(45, 66)(47, 52)(49, 76)(53, 60)(54, 62)(56, 61)(57,
        90)(58, 112)(59, 70)(63, 85)(64, 95)(67, 73)(69, 114)(75, 106)(78, 
        99)(80, 109)(82, 89)(84, 104)(93, 107)(97, 101)
]
,
[
    G!(1, 9)(2, 19)(3, 12)(4, 14)(5, 50)(6, 22)(7, 80)(8, 42)(10, 17)(11, 37)(13, 
        55)(15, 20)(16, 33)(18, 64)(21, 109)(23, 52)(24, 51)(25, 119)(26, 
        84)(27, 66)(28, 29)(30, 54)(31, 85)(32, 89)(34, 83)(35, 99)(36, 92)(38, 
        67)(39, 65)(40, 110)(43, 96)(45, 97)(46, 104)(48, 86)(49, 77)(53, 
        59)(56, 103)(57, 105)(58, 107)(60, 113)(61, 102)(63, 95)(69, 101)(71, 
        93)(73, 106)(74, 111)(75, 90)(76, 79)(78, 88)(82, 108)(87, 91)(94, 
        118)(98, 112)(100, 115)(114, 117)(116, 120),
    G!(1, 114)(2, 23)(4, 115)(5, 41)(6, 81)(7, 32)(8, 33)(9, 104)(10, 48)(12, 
        119)(13, 92)(14, 55)(15, 97)(16, 118)(17, 35)(18, 45)(19, 69)(20, 
        31)(21, 29)(22, 28)(24, 49)(25, 65)(27, 72)(30, 79)(36, 50)(37, 117)(38,
        89)(39, 51)(40, 43)(42, 108)(44, 95)(46, 98)(47, 56)(52, 88)(53, 73)(54,
        68)(57, 86)(59, 64)(60, 111)(61, 113)(62, 100)(63, 74)(66, 116)(67, 
        71)(70, 110)(75, 94)(76, 109)(77, 107)(78, 99)(80, 105)(83, 90)(84, 
        112)(87, 96)(91, 120)(93, 101)(102, 103),
    G!(1, 22)(2, 10)(3, 88)(4, 53)(5, 96)(6, 114)(7, 62)(8, 107)(9, 44)(12, 
        46)(13, 66)(14, 113)(16, 109)(17, 25)(18, 24)(19, 39)(20, 79)(21, 
        71)(23, 73)(26, 41)(27, 93)(28, 90)(29, 57)(30, 108)(31, 72)(32, 
        120)(33, 110)(36, 77)(37, 115)(38, 76)(40, 60)(42, 43)(45, 67)(47, 
        49)(48, 75)(50, 70)(51, 69)(54, 55)(56, 86)(58, 85)(59, 91)(61, 84)(63, 
        94)(64, 100)(68, 103)(74, 112)(80, 111)(81, 105)(82, 87)(83, 101)(92, 
        98)(95, 99)(97, 106)(102, 117)(104, 118)(116, 119)
]
,
[
    G!(2, 66)(4, 73)(5, 104)(6, 51)(7, 102)(8, 47)(9, 80)(10, 26)(11, 120)(12, 
        71)(13, 37)(14, 117)(15, 107)(16, 98)(17, 101)(18, 44)(19, 113)(20, 
        103)(21, 23)(22, 49)(24, 46)(25, 30)(27, 119)(28, 89)(29, 110)(31, 
        40)(32, 86)(33, 97)(34, 45)(35, 106)(36, 105)(38, 118)(39, 43)(41, 
        96)(42, 116)(48, 59)(50, 77)(52, 74)(53, 111)(54, 90)(55, 88)(56, 
        63)(58, 81)(61, 95)(62, 93)(67, 72)(69, 84)(70, 108)(75, 82)(76, 
        115)(78, 92)(79, 112)(83, 85)(87, 99)(91, 114)(100, 109),
    G!(1, 93)(2, 63)(3, 74)(4, 109)(5, 31)(6, 25)(7, 43)(8, 17)(9, 20)(10, 36)(11,
        40)(12, 32)(13, 44)(14, 95)(15, 118)(16, 50)(18, 49)(19, 120)(21, 
        112)(22, 35)(23, 59)(24, 98)(26, 62)(27, 47)(28, 60)(29, 78)(30, 48)(34,
        70)(37, 96)(38, 73)(39, 53)(41, 85)(45, 58)(46, 55)(51, 116)(52, 
        100)(56, 91)(57, 107)(61, 67)(64, 84)(65, 113)(66, 75)(68, 92)(69, 
        104)(71, 87)(76, 90)(80, 97)(81, 106)(82, 89)(83, 86)(88, 115)(94, 
        114)(99, 108)(103, 117)(105, 110)(111, 119),
    G!(1, 54)(2, 11)(3, 92)(4, 96)(5, 56)(6, 84)(7, 26)(8, 116)(9, 31)(10, 20)(12,
        70)(13, 59)(14, 69)(15, 81)(16, 78)(17, 32)(18, 28)(21, 41)(22, 119)(23,
        36)(24, 71)(25, 63)(27, 109)(29, 30)(34, 51)(35, 107)(37, 86)(38, 
        88)(39, 72)(40, 53)(42, 64)(43, 114)(44, 85)(45, 65)(46, 58)(47, 83)(48,
        113)(49, 103)(50, 105)(52, 104)(55, 98)(57, 91)(60, 89)(61, 111)(62, 
        110)(66, 95)(67, 112)(68, 75)(73, 115)(74, 100)(79, 99)(82, 117)(87, 
        94)(90, 118)(93, 102)(97, 101)
]
,
[
    G!(1, 18)(2, 114)(3, 87)(4, 59)(6, 34)(7, 30)(8, 79)(9, 66)(10, 32)(11, 
        54)(12, 112)(13, 48)(14, 65)(15, 27)(16, 74)(17, 108)(19, 21)(20, 
        64)(22, 39)(23, 82)(24, 46)(25, 33)(26, 119)(28, 81)(31, 55)(35, 92)(36,
        51)(37, 67)(38, 80)(40, 88)(41, 69)(42, 115)(45, 84)(47, 106)(49, 
        93)(50, 68)(52, 110)(53, 71)(56, 96)(57, 120)(58, 95)(60, 90)(61, 
        89)(63, 105)(70, 72)(73, 101)(75, 113)(76, 86)(77, 99)(78, 111)(83, 
        118)(85, 100)(91, 109)(94, 104)(97, 102)(107, 116),
    G!(1, 35)(2, 50)(3, 84)(4, 28)(5, 10)(6, 22)(8, 29)(9, 52)(11, 62)(12, 54)(13,
        24)(14, 101)(15, 82)(16, 17)(18, 94)(19, 55)(20, 38)(21, 104)(23, 
        96)(25, 26)(27, 63)(30, 92)(32, 53)(33, 106)(34, 47)(36, 43)(37, 45)(39,
        42)(40, 107)(44, 87)(46, 120)(48, 66)(51, 90)(56, 75)(57, 93)(58, 
        98)(59, 71)(60, 67)(64, 77)(65, 108)(68, 89)(69, 113)(70, 78)(72, 
        76)(73, 103)(74, 102)(79, 116)(80, 86)(81, 95)(83, 100)(85, 114)(88, 
        112)(91, 118)(97, 117)(99, 119)(111, 115),
    G!(1, 29)(2, 120)(3, 23)(4, 81)(5, 63)(6, 30)(7, 115)(8, 102)(9, 103)(10, 
        11)(12, 15)(13, 113)(14, 36)(16, 28)(17, 53)(18, 32)(19, 31)(20, 
        106)(22, 70)(24, 91)(25, 80)(26, 46)(27, 55)(33, 56)(34, 119)(35, 
        87)(37, 58)(40, 74)(41, 67)(43, 57)(44, 47)(45, 88)(48, 118)(49, 
        108)(50, 86)(51, 99)(52, 73)(54, 114)(59, 116)(60, 61)(62, 65)(64, 
        89)(66, 90)(68, 98)(69, 107)(71, 84)(72, 112)(76, 77)(78, 97)(79, 
        96)(82, 94)(83, 85)(92, 117)(93, 95)(100, 101)(104, 105)
]
,
[
    G!(1, 29)(2, 73)(3, 113)(4, 115)(5, 94)(6, 27)(7, 21)(8, 88)(9, 26)(10, 
        38)(12, 31)(13, 86)(15, 41)(17, 109)(18, 20)(19, 81)(22, 43)(23, 99)(24,
        90)(25, 87)(28, 30)(32, 114)(33, 95)(34, 118)(35, 112)(36, 63)(37, 
        96)(39, 93)(40, 79)(42, 67)(44, 52)(45, 119)(46, 120)(47, 71)(48, 
        107)(49, 62)(50, 102)(51, 80)(53, 78)(55, 106)(56, 108)(57, 60)(58, 
        68)(59, 91)(64, 98)(65, 117)(66, 116)(69, 72)(70, 85)(74, 103)(75, 
        97)(76, 84)(77, 89)(83, 100)(92, 111)(101, 105),
    G!(1, 113)(2, 70)(4, 94)(5, 49)(6, 73)(8, 107)(9, 52)(10, 102)(11, 69)(12, 
        14)(13, 33)(15, 16)(17, 57)(18, 64)(19, 34)(20, 75)(21, 47)(22, 46)(23, 
        42)(24, 87)(25, 86)(26, 120)(27, 108)(28, 36)(29, 56)(30, 103)(31, 
        90)(32, 45)(35, 62)(37, 98)(38, 99)(40, 48)(41, 67)(43, 114)(50, 
        117)(53, 54)(55, 63)(58, 95)(60, 79)(61, 84)(65, 91)(66, 119)(68, 
        93)(71, 96)(72, 77)(74, 105)(76, 85)(78, 97)(80, 92)(81, 101)(82, 
        100)(83, 112)(88, 89)(104, 118)(110, 116)(111, 115),
    G!(1, 59)(2, 72)(4, 34)(5, 87)(6, 18)(7, 84)(8, 63)(9, 108)(10, 32)(11, 
        30)(12, 70)(13, 98)(14, 24)(15, 22)(16, 33)(17, 111)(20, 64)(21, 29)(23,
        38)(25, 61)(26, 93)(27, 104)(28, 105)(35, 102)(36, 52)(37, 97)(39, 
        94)(40, 65)(41, 56)(42, 116)(44, 85)(45, 54)(46, 88)(47, 96)(49, 77)(50,
        107)(51, 83)(53, 82)(55, 117)(57, 109)(58, 91)(60, 113)(62, 86)(66, 
        78)(67, 92)(68, 115)(69, 106)(71, 80)(73, 90)(74, 89)(75, 101)(79, 
        81)(95, 120)(99, 119)(110, 118)(112, 114)
]
,
[
    G!(1, 35)(2, 3)(4, 76)(5, 71)(6, 68)(8, 119)(10, 46)(11, 111)(12, 91)(13, 
        24)(14, 37)(15, 80)(16, 59)(17, 116)(18, 63)(19, 98)(20, 40)(21, 53)(22,
        89)(23, 103)(25, 73)(26, 96)(27, 95)(28, 72)(29, 99)(30, 87)(32, 85)(33,
        120)(34, 36)(38, 58)(39, 88)(41, 110)(42, 74)(43, 66)(44, 60)(45, 
        101)(47, 108)(48, 75)(49, 57)(52, 84)(54, 107)(55, 118)(56, 64)(61, 
        78)(62, 115)(65, 77)(67, 112)(69, 113)(79, 106)(81, 94)(82, 86)(83, 
        105)(92, 102)(93, 100)(104, 114)(109, 117),
    G!(1, 41)(2, 40)(3, 32)(4, 67)(5, 18)(6, 38)(7, 13)(8, 11)(9, 72)(10, 23)(12, 
        29)(14, 107)(15, 25)(17, 98)(19, 28)(21, 33)(22, 116)(24, 120)(27, 
        50)(30, 35)(31, 92)(34, 49)(36, 115)(37, 93)(39, 86)(42, 55)(43, 
        110)(44, 108)(45, 66)(46, 77)(48, 57)(51, 54)(52, 114)(53, 83)(56, 
        89)(58, 99)(59, 104)(60, 71)(61, 97)(63, 100)(64, 111)(65, 76)(68, 
        70)(69, 88)(73, 96)(74, 78)(75, 118)(79, 95)(80, 94)(81, 82)(84, 91)(85,
        105)(87, 109)(90, 113)(101, 102)(103, 106),
    G!(1, 88)(2, 22)(3, 72)(4, 77)(5, 120)(6, 47)(7, 52)(8, 114)(9, 108)(10, 
        73)(11, 13)(14, 24)(16, 94)(17, 39)(18, 76)(19, 46)(20, 66)(21, 110)(23,
        112)(25, 78)(26, 54)(27, 82)(28, 57)(29, 45)(30, 90)(31, 102)(32, 
        50)(33, 91)(34, 68)(35, 70)(36, 40)(37, 97)(38, 95)(41, 43)(42, 93)(44, 
        81)(49, 51)(55, 109)(56, 99)(58, 92)(60, 65)(61, 85)(62, 83)(63, 87)(64,
        79)(67, 111)(69, 84)(71, 89)(74, 117)(75, 101)(80, 105)(86, 115)(98, 
        107)(103, 104)(106, 113)(116, 118)
]
,
[
    G!(1, 30)(2, 120)(3, 36)(4, 94)(5, 49)(6, 15)(7, 77)(8, 34)(9, 103)(10, 
        31)(11, 26)(12, 14)(13, 23)(16, 99)(17, 91)(18, 116)(19, 86)(20, 73)(21,
        88)(22, 57)(24, 53)(25, 80)(27, 65)(28, 51)(29, 113)(32, 95)(35, 
        100)(38, 75)(40, 83)(41, 67)(43, 114)(44, 59)(46, 108)(47, 48)(50, 
        63)(52, 56)(54, 71)(55, 62)(60, 61)(64, 110)(66, 69)(68, 111)(70, 
        119)(72, 109)(74, 85)(76, 105)(78, 118)(79, 90)(81, 96)(82, 117)(84, 
        102)(87, 101)(89, 112)(92, 107)(93, 97)(104, 115),
    G!(1, 6)(2, 61)(3, 78)(5, 74)(7, 101)(8, 60)(10, 114)(11, 113)(12, 96)(13, 
        73)(14, 100)(15, 79)(16, 21)(17, 33)(18, 53)(19, 103)(20, 41)(22, 
        44)(23, 105)(24, 48)(25, 72)(26, 57)(27, 104)(28, 75)(29, 106)(30, 
        67)(32, 89)(34, 83)(35, 82)(36, 98)(37, 40)(38, 84)(39, 95)(42, 71)(43, 
        66)(45, 90)(46, 88)(49, 77)(50, 118)(52, 54)(55, 97)(56, 64)(58, 
        117)(59, 102)(62, 86)(63, 92)(65, 91)(68, 115)(69, 111)(80, 94)(81, 
        99)(85, 119)(87, 112)(93, 110)(107, 109)(116, 120),
    G!(2, 100)(3, 77)(4, 119)(5, 62)(6, 40)(7, 21)(8, 92)(9, 109)(10, 91)(11, 
        19)(12, 116)(13, 83)(15, 73)(16, 110)(17, 80)(18, 20)(22, 94)(23, 
        113)(24, 50)(25, 120)(26, 67)(27, 96)(28, 30)(29, 98)(31, 35)(32, 
        72)(33, 95)(34, 108)(36, 48)(37, 78)(38, 88)(41, 86)(42, 51)(43, 
        117)(44, 103)(45, 56)(46, 87)(47, 105)(49, 65)(53, 79)(54, 81)(55, 
        71)(57, 61)(58, 89)(59, 111)(60, 82)(63, 69)(66, 70)(68, 99)(75, 97)(76,
        106)(84, 101)(85, 112)(90, 102)(107, 114)(115, 118)
]
,
[
    G!(1, 75)(2, 48)(3, 49)(4, 99)(7, 58)(8, 112)(9, 54)(10, 52)(11, 105)(12, 
        104)(13, 21)(14, 118)(15, 60)(16, 101)(17, 81)(18, 44)(19, 79)(20, 
        30)(22, 93)(23, 47)(25, 53)(26, 61)(28, 78)(29, 84)(31, 82)(32, 76)(33, 
        88)(34, 110)(35, 94)(36, 89)(37, 120)(38, 43)(39, 87)(40, 55)(41, 
        106)(42, 97)(45, 59)(46, 117)(50, 68)(51, 71)(56, 90)(57, 116)(62, 
        72)(63, 80)(65, 114)(66, 70)(67, 96)(69, 102)(74, 86)(77, 91)(83, 
        108)(85, 109)(92, 111)(98, 100)(103, 113)(115, 119),
    G!(1, 19)(2, 88)(4, 11)(5, 110)(8, 119)(9, 33)(10, 30)(12, 72)(13, 89)(14, 
        66)(15, 70)(16, 105)(17, 44)(18, 54)(20, 32)(21, 29)(22, 52)(23, 87)(24,
        92)(25, 51)(27, 63)(28, 107)(31, 84)(34, 81)(35, 40)(36, 37)(38, 56)(39,
        86)(41, 116)(42, 96)(43, 95)(45, 114)(46, 97)(47, 118)(48, 69)(49, 
        80)(50, 71)(53, 76)(55, 98)(57, 109)(58, 111)(59, 106)(61, 73)(62, 
        101)(64, 115)(65, 113)(67, 117)(68, 79)(74, 78)(75, 85)(77, 108)(82, 
        120)(83, 90)(91, 94)(93, 103)(99, 104),
    G!(1, 38)(2, 57)(3, 107)(4, 16)(5, 75)(6, 83)(7, 23)(8, 44)(9, 88)(10, 24)(11,
        59)(12, 58)(14, 36)(15, 54)(17, 82)(18, 22)(19, 105)(20, 102)(21, 
        56)(25, 77)(26, 37)(27, 35)(28, 76)(29, 90)(30, 93)(31, 60)(32, 92)(33, 
        119)(34, 108)(39, 74)(40, 104)(41, 115)(42, 62)(43, 112)(45, 64)(46, 
        80)(47, 79)(48, 113)(49, 99)(50, 100)(51, 65)(52, 89)(53, 97)(61, 
        71)(66, 110)(67, 118)(68, 101)(70, 72)(73, 81)(78, 94)(84, 111)(85, 
        86)(87, 96)(95, 120)(98, 117)(103, 114)
]
,
[
    G!(1, 23)(2, 75)(3, 7)(4, 92)(5, 115)(6, 59)(8, 77)(9, 43)(10, 79)(11, 
        117)(12, 38)(13, 65)(14, 119)(15, 40)(16, 35)(18, 97)(19, 105)(20, 
        70)(22, 32)(24, 94)(25, 90)(26, 44)(27, 28)(29, 104)(30, 84)(31, 68)(33,
        114)(34, 71)(36, 118)(37, 47)(39, 100)(41, 58)(42, 76)(45, 116)(46, 
        85)(48, 88)(49, 81)(50, 62)(51, 102)(52, 95)(53, 74)(54, 78)(56, 72)(57,
        61)(60, 109)(63, 98)(64, 96)(67, 91)(69, 89)(73, 120)(80, 101)(82, 
        83)(87, 111)(106, 112)(107, 108)(110, 113),
    G!(1, 25)(3, 47)(5, 71)(6, 35)(7, 117)(8, 97)(9, 18)(10, 58)(11, 87)(12, 
        96)(13, 74)(14, 34)(15, 64)(16, 90)(17, 57)(19, 72)(20, 82)(21, 94)(22, 
        53)(23, 113)(24, 83)(26, 120)(27, 66)(28, 37)(29, 80)(30, 112)(31, 
        79)(32, 107)(33, 75)(36, 73)(38, 101)(39, 114)(40, 116)(41, 103)(42, 
        110)(43, 70)(45, 63)(48, 86)(49, 77)(50, 118)(52, 60)(54, 109)(55, 
        89)(59, 99)(61, 119)(62, 68)(65, 91)(67, 69)(76, 85)(78, 88)(84, 95)(92,
        106)(93, 98)(100, 115)(102, 108)(105, 111),
    G!(1, 119)(2, 10)(3, 4)(5, 106)(6, 13)(7, 98)(8, 16)(9, 25)(11, 76)(12, 
        52)(14, 96)(15, 39)(17, 113)(18, 91)(19, 99)(20, 36)(21, 118)(22, 
        90)(23, 60)(24, 55)(26, 43)(27, 86)(28, 101)(29, 50)(30, 65)(31, 
        102)(32, 110)(33, 103)(34, 74)(35, 56)(37, 100)(38, 92)(42, 84)(44, 
        120)(45, 46)(47, 68)(48, 78)(49, 97)(51, 75)(53, 111)(54, 108)(58, 
        116)(61, 112)(62, 105)(64, 85)(66, 109)(67, 82)(69, 73)(70, 95)(71, 
        115)(72, 107)(79, 93)(80, 117)(83, 104)(87, 94)(88, 114)
]
,
[
    G!(1, 25)(2, 24)(3, 43)(4, 103)(5, 11)(6, 35)(7, 36)(8, 57)(9, 15)(10, 
        110)(13, 111)(14, 56)(16, 58)(17, 105)(18, 48)(19, 51)(20, 82)(21, 
        69)(23, 32)(26, 116)(27, 78)(28, 93)(29, 112)(30, 87)(31, 79)(33, 
        45)(37, 54)(38, 109)(39, 71)(40, 42)(41, 72)(46, 104)(47, 49)(50, 
        91)(52, 95)(53, 62)(55, 120)(59, 68)(60, 97)(61, 86)(63, 75)(64, 
        115)(65, 98)(66, 88)(67, 94)(70, 77)(73, 117)(74, 84)(76, 85)(80, 
        106)(89, 90)(92, 114)(100, 102)(101, 118)(107, 113)(108, 119),
    G!(1, 93)(2, 8)(4, 109)(5, 110)(6, 32)(7, 57)(9, 41)(10, 85)(12, 72)(13, 
        119)(14, 52)(15, 38)(16, 117)(17, 84)(18, 62)(19, 120)(20, 43)(21, 
        46)(22, 29)(23, 87)(24, 28)(26, 48)(27, 105)(30, 60)(31, 59)(33, 99)(34,
        53)(35, 112)(36, 107)(37, 55)(39, 64)(40, 51)(42, 116)(44, 65)(45, 
        114)(47, 71)(49, 98)(50, 89)(56, 67)(58, 82)(61, 113)(63, 70)(66, 
        108)(69, 79)(73, 106)(74, 104)(76, 115)(77, 97)(78, 96)(80, 92)(81, 
        90)(83, 86)(88, 118)(91, 111)(94, 103)(100, 101),
    G!(1, 31)(2, 3)(4, 82)(5, 55)(6, 86)(7, 69)(8, 41)(10, 88)(12, 39)(13, 24)(14,
        37)(15, 89)(16, 102)(17, 38)(18, 21)(19, 92)(20, 60)(22, 28)(23, 53)(25,
        94)(26, 104)(27, 114)(29, 119)(30, 116)(32, 81)(33, 54)(34, 36)(40, 
        79)(42, 71)(43, 66)(44, 106)(45, 101)(46, 91)(47, 108)(48, 75)(49, 
        57)(51, 62)(52, 84)(56, 64)(58, 87)(59, 98)(61, 78)(63, 103)(65, 77)(67,
        120)(68, 76)(72, 80)(73, 85)(74, 118)(83, 105)(90, 111)(93, 100)(95, 
        96)(99, 110)(107, 112)(109, 117)
]
,
[
    G!(1, 32)(2, 8)(3, 64)(4, 114)(5, 84)(6, 115)(7, 72)(9, 28)(10, 31)(11, 
        107)(12, 58)(14, 20)(15, 85)(17, 41)(18, 116)(19, 119)(22, 54)(23, 
        78)(24, 53)(25, 27)(26, 60)(29, 89)(30, 33)(34, 71)(35, 43)(36, 105)(38,
        109)(42, 44)(45, 118)(46, 90)(47, 110)(48, 97)(49, 79)(50, 102)(51, 
        75)(52, 83)(55, 120)(56, 98)(57, 62)(59, 88)(61, 86)(63, 108)(65, 
        82)(66, 80)(67, 100)(68, 106)(69, 96)(70, 92)(74, 113)(76, 93)(77, 
        103)(81, 117)(87, 101)(91, 94)(99, 111)(104, 112),
    G!(1, 74)(2, 6)(3, 67)(4, 95)(5, 79)(7, 60)(8, 62)(9, 36)(11, 47)(12, 80)(14, 
        52)(15, 16)(17, 76)(18, 32)(19, 59)(20, 118)(21, 61)(22, 53)(23, 87)(24,
        113)(25, 112)(26, 68)(28, 46)(29, 42)(30, 50)(31, 55)(33, 107)(34, 
        116)(37, 120)(38, 63)(39, 104)(40, 69)(41, 99)(43, 101)(44, 115)(45, 
        83)(49, 66)(51, 110)(54, 85)(57, 89)(58, 82)(64, 93)(65, 84)(70, 
        117)(72, 103)(73, 98)(75, 119)(77, 86)(78, 81)(88, 100)(90, 111)(91, 
        96)(92, 94)(97, 114)(102, 105)(106, 108),
    G!(1, 88)(2, 84)(3, 27)(4, 109)(5, 40)(6, 95)(7, 36)(8, 120)(9, 39)(10, 
        30)(11, 33)(13, 91)(14, 101)(15, 96)(16, 77)(17, 24)(18, 21)(19, 
        112)(20, 57)(22, 60)(23, 47)(25, 94)(26, 106)(28, 49)(29, 70)(31, 
        116)(32, 92)(34, 64)(35, 93)(37, 63)(38, 46)(41, 43)(42, 104)(44, 
        71)(45, 103)(48, 53)(50, 58)(51, 111)(52, 114)(55, 78)(56, 69)(61, 
        79)(62, 85)(65, 99)(66, 67)(68, 83)(72, 82)(73, 90)(74, 105)(75, 
        108)(76, 118)(80, 117)(81, 107)(86, 89)(98, 115)(102, 110)
]

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;