P:=PermutationGroup<693 | \[ 1, 2, 422, 144, 529, 166, 672, 466, 571, 141, 578, 48, 99, 35, 596, 632, 296, 289, 19, 116, 252, 260, 60, 77, 534, 85, 71, 563, 324, 645, 31, 62, 547, 354, 14, 273, 124, 357, 39, 671, 644, 45, 403, 207, 42, 46, 628, 12, 487, 457, 651, 168, 291, 553, 669, 575, 352, 608, 187, 23, 160, 32, 109, 682, 336, 615, 686, 277, 69, 542, 27, 233, 602, 74, 250, 531, 24, 548, 276, 80, 305, 366, 600, 115, 26, 327, 185, 88, 397, 237, 448, 298, 445, 314, 161, 479, 231, 494, 13, 685, 402, 501, 143, 657, 195, 372, 539, 638, 63, 637, 587, 528, 147, 165, 84, 20, 152, 474, 465, 643, 630, 370, 229, 37, 514, 316, 665, 580, 375, 415, 261, 132, 653, 371, 590, 241, 666, 163, 170, 398, 10, 490, 103, 4, 593, 513, 113, 621, 149, 511, 320, 117, 425, 485, 155, 361, 248, 537, 460, 61, 95, 416, 138, 565, 114, 6, 581, 52, 464, 139, 315, 478, 232, 217, 476, 176, 216, 329, 640, 322, 572, 523, 269, 480, 87, 200, 59, 573, 307, 679, 243, 192, 492, 225, 105, 522, 349, 297, 332, 186, 378, 280, 458, 391, 690, 236, 44, 399, 502, 406, 211, 518, 461, 214, 658, 177, 174, 244, 577, 220, 620, 267, 317, 504, 194, 356, 227, 338, 123, 343, 97, 173, 72, 595, 516, 206, 90, 673, 507, 240, 136, 433, 191, 218, 471, 527, 660, 157, 500, 75, 647, 21, 622, 535, 524, 583, 257, 683, 294, 22, 131, 543, 263, 264, 489, 481, 222, 631, 183, 270, 271, 272, 36, 649, 659, 79, 68, 279, 278, 202, 434, 282, 339, 532, 503, 668, 401, 477, 18, 558, 53, 456, 444, 259, 344, 17, 198, 92, 545, 584, 484, 606, 689, 455, 81, 420, 189, 308, 677, 564, 311, 312, 557, 94, 171, 126, 223, 684, 421, 151, 453, 180, 508, 29, 396, 450, 86, 405, 178, 486, 380, 199, 568, 634, 335, 65, 530, 228, 283, 623, 588, 678, 230, 295, 419, 346, 385, 348, 197, 350, 351, 57, 603, 34, 648, 226, 38, 358, 384, 360, 156, 424, 363, 589, 680, 82, 470, 368, 520, 122, 134, 106, 389, 655, 129, 591, 546, 201, 597, 331, 441, 428, 459, 359, 347, 386, 681, 688, 373, 390, 204, 493, 393, 495, 601, 325, 89, 140, 208, 636, 287, 101, 43, 404, 328, 210, 536, 408, 604, 635, 411, 579, 451, 566, 130, 162, 417, 639, 345, 306, 319, 3, 517, 362, 153, 560, 427, 382, 429, 554, 438, 435, 242, 281, 432, 447, 512, 431, 442, 619, 381, 439, 674, 293, 93, 446, 436, 91, 594, 326, 413, 562, 321, 454, 304, 292, 50, 203, 383, 159, 213, 662, 559, 169, 119, 8, 483, 468, 585, 367, 245, 627, 611, 118, 506, 175, 288, 172, 96, 184, 266, 482, 467, 301, 154, 330, 49, 626, 265, 142, 656, 193, 392, 98, 394, 540, 612, 549, 499, 249, 102, 209, 285, 224, 505, 475, 239, 323, 519, 654, 150, 437, 146, 125, 624, 235, 423, 212, 509, 369, 610, 196, 182, 255, 567, 526, 246, 112, 5, 337, 76, 284, 661, 25, 254, 407, 158, 652, 107, 496, 613, 70, 262, 544, 299, 377, 33, 78, 498, 555, 616, 614, 54, 430, 550, 670, 313, 290, 463, 426, 561, 452, 28, 310, 164, 414, 525, 333, 617, 692, 9, 181, 188, 574, 56, 576, 219, 11, 412, 128, 167, 582, 256, 300, 469, 650, 111, 341, 364, 135, 376, 663, 145, 449, 234, 15, 379, 646, 599, 83, 395, 73, 353, 409, 605, 302, 607, 58, 676, 521, 473, 497, 541, 552, 66, 551, 569, 618, 440, 221, 148, 253, 340, 515, 625, 488, 472, 47, 633, 121, 268, 16, 629, 334, 410, 400, 110, 108, 418, 179, 641, 691, 120, 41, 30, 598, 251, 355, 274, 586, 51, 538, 133, 510, 374, 491, 104, 215, 275, 247, 533, 462, 592, 664, 127, 137, 667, 286, 55, 556, 40, 7, 238, 443, 675, 609, 309, 342, 190, 365, 387, 64, 258, 318, 100, 67, 693, 388, 303, 205, 642, 570, 687 ], \[ 1, 309, 515, 397, 275, 6, 156, 66, 26, 60, 504, 361, 216, 123, 380, 423, 94, 449, 411, 143, 349, 202, 23, 162, 370, 9, 671, 266, 476, 305, 240, 303, 572, 195, 35, 517, 221, 431, 338, 567, 649, 207, 536, 197, 252, 446, 47, 173, 346, 445, 483, 267, 148, 424, 72, 564, 470, 624, 259, 10, 548, 188, 167, 323, 404, 8, 175, 234, 129, 222, 183, 55, 422, 393, 563, 210, 144, 78, 395, 228, 191, 82, 439, 420, 584, 137, 238, 511, 416, 180, 464, 92, 595, 17, 560, 297, 378, 98, 103, 620, 333, 629, 99, 104, 610, 139, 538, 447, 152, 626, 366, 112, 541, 300, 276, 177, 204, 347, 119, 134, 556, 122, 14, 125, 124, 440, 583, 322, 69, 320, 310, 350, 343, 120, 496, 562, 86, 413, 106, 623, 141, 286, 20, 77, 145, 326, 638, 53, 429, 625, 247, 109, 627, 194, 155, 7, 409, 686, 577, 160, 161, 24, 385, 596, 571, 456, 63, 458, 169, 357, 658, 578, 48, 455, 67, 675, 116, 243, 506, 90, 198, 622, 71, 261, 615, 481, 314, 62, 478, 475, 81, 192, 193, 154, 34, 679, 44, 181, 664, 250, 467, 22, 542, 117, 591, 495, 42, 331, 585, 76, 283, 271, 355, 607, 540, 13, 217, 356, 619, 336, 37, 70, 280, 307, 225, 569, 482, 80, 229, 291, 651, 672, 588, 68, 497, 469, 634, 87, 368, 31, 452, 242, 178, 503, 359, 606, 151, 691, 443, 200, 401, 45, 594, 530, 604, 256, 272, 609, 59, 396, 184, 264, 505, 262, 656, 28, 52, 532, 525, 544, 212, 257, 688, 412, 5, 115, 457, 646, 652, 223, 281, 282, 211, 295, 617, 142, 407, 288, 523, 568, 230, 292, 614, 296, 284, 294, 96, 477, 345, 114, 612, 674, 32, 304, 30, 601, 224, 518, 2, 131, 360, 667, 636, 187, 590, 460, 325, 549, 381, 130, 321, 128, 64, 537, 317, 146, 327, 354, 645, 508, 208, 499, 101, 580, 363, 220, 406, 39, 358, 533, 462, 661, 133, 546, 299, 49, 118, 427, 21, 132, 599, 557, 353, 328, 213, 218, 170, 339, 245, 311, 12, 471, 335, 364, 365, 111, 400, 239, 369, 25, 376, 438, 684, 545, 408, 371, 631, 97, 498, 15, 319, 386, 383, 553, 163, 382, 459, 632, 597, 390, 581, 650, 74, 502, 79, 260, 4, 678, 565, 367, 251, 510, 647, 65, 521, 337, 287, 375, 157, 657, 19, 274, 138, 414, 663, 89, 417, 644, 559, 84, 683, 73, 16, 54, 630, 426, 348, 468, 149, 552, 38, 484, 687, 628, 516, 613, 486, 372, 83, 126, 676, 461, 249, 519, 50, 46, 108, 448, 18, 513, 474, 241, 603, 454, 174, 166, 277, 168, 387, 316, 442, 341, 655, 91, 465, 673, 201, 428, 236, 57, 362, 670, 473, 451, 190, 29, 298, 189, 547, 575, 186, 227, 51, 432, 485, 437, 526, 488, 489, 668, 491, 492, 633, 494, 206, 135, 235, 379, 332, 527, 586, 394, 244, 11, 263, 179, 618, 330, 554, 402, 88, 682, 450, 685, 3, 435, 36, 308, 444, 566, 405, 640, 289, 642, 269, 487, 500, 528, 529, 254, 535, 268, 340, 534, 531, 43, 324, 107, 598, 215, 113, 203, 576, 270, 374, 344, 479, 61, 318, 550, 689, 430, 384, 509, 555, 121, 352, 654, 419, 95, 605, 136, 75, 56, 399, 520, 40, 290, 226, 680, 165, 33, 616, 574, 480, 543, 159, 172, 639, 334, 391, 677, 127, 85, 209, 501, 587, 233, 593, 315, 205, 660, 589, 253, 93, 164, 389, 539, 351, 648, 306, 608, 453, 255, 561, 246, 214, 602, 258, 105, 611, 301, 436, 293, 185, 573, 285, 507, 219, 100, 653, 182, 140, 58, 150, 110, 153, 434, 102, 425, 377, 388, 493, 237, 635, 313, 637, 147, 579, 522, 641, 524, 690, 418, 329, 278, 403, 600, 41, 392, 231, 279, 621, 558, 463, 265, 410, 171, 659, 592, 342, 669, 415, 199, 665, 666, 312, 490, 662, 472, 27, 232, 466, 302, 176, 441, 582, 398, 196, 570, 681, 512, 421, 373, 514, 158, 433, 273, 551, 643, 248, 692, 693 ], \[ 1, 598, 293, 645, 559, 663, 521, 527, 210, 634, 579, 345, 507, 25, 247, 136, 21, 299, 363, 212, 17, 330, 334, 666, 14, 511, 600, 28, 362, 63, 31, 570, 563, 589, 534, 465, 301, 88, 646, 80, 185, 259, 186, 187, 45, 482, 463, 678, 302, 673, 588, 659, 539, 54, 626, 408, 615, 161, 59, 388, 436, 365, 30, 64, 249, 636, 209, 404, 372, 253, 653, 614, 378, 561, 290, 431, 111, 447, 637, 40, 268, 415, 525, 444, 239, 130, 443, 38, 208, 562, 416, 662, 468, 349, 601, 481, 420, 658, 150, 202, 101, 355, 347, 669, 622, 271, 213, 473, 329, 515, 77, 627, 680, 129, 509, 375, 164, 310, 580, 426, 513, 122, 123, 512, 317, 471, 556, 193, 114, 86, 625, 411, 567, 488, 450, 16, 167, 170, 531, 529, 688, 541, 535, 178, 655, 590, 692, 392, 270, 99, 191, 399, 491, 154, 282, 419, 621, 553, 686, 616, 58, 292, 438, 117, 518, 295, 137, 434, 344, 138, 489, 595, 458, 423, 316, 505, 406, 144, 179, 455, 558, 542, 576, 530, 41, 43, 44, 611, 644, 190, 151, 417, 128, 687, 523, 503, 197, 403, 500, 654, 306, 100, 672, 456, 483, 206, 207, 89, 67, 9, 652, 20, 107, 335, 528, 413, 322, 218, 219, 557, 486, 566, 223, 400, 693, 506, 263, 586, 229, 255, 602, 610, 430, 238, 508, 440, 241, 234, 85, 311, 237, 242, 631, 679, 585, 578, 15, 442, 65, 647, 572, 252, 70, 584, 230, 670, 393, 549, 42, 612, 368, 629, 227, 538, 425, 266, 364, 81, 358, 149, 106, 599, 492, 487, 405, 410, 499, 461, 291, 280, 328, 155, 604, 596, 285, 303, 287, 395, 533, 75, 279, 162, 3, 294, 166, 296, 510, 643, 18, 385, 37, 49, 286, 517, 320, 201, 674, 575, 650, 118, 240, 348, 664, 314, 656, 175, 125, 318, 597, 305, 321, 217, 323, 324, 484, 630, 546, 281, 109, 22, 660, 418, 333, 23, 214, 639, 564, 691, 633, 593, 467, 361, 501, 169, 12, 367, 103, 312, 94, 607, 605, 504, 681, 414, 102, 356, 618, 269, 460, 360, 342, 29, 19, 267, 62, 377, 346, 261, 623, 370, 657, 69, 373, 520, 116, 554, 366, 73, 379, 532, 389, 649, 383, 502, 300, 470, 603, 60, 381, 454, 448, 148, 257, 577, 288, 437, 565, 628, 152, 224, 568, 536, 198, 68, 275, 177, 407, 56, 543, 276, 132, 466, 216, 354, 82, 91, 192, 332, 156, 97, 421, 519, 174, 424, 265, 120, 427, 606, 429, 233, 76, 682, 433, 168, 435, 61, 396, 163, 493, 236, 441, 248, 87, 84, 526, 675, 78, 391, 661, 135, 571, 632, 453, 390, 180, 204, 478, 173, 459, 359, 278, 560, 47, 592, 36, 412, 341, 93, 476, 386, 126, 494, 108, 480, 475, 469, 608, 457, 479, 474, 96, 46, 205, 325, 485, 221, 274, 134, 171, 689, 153, 273, 439, 472, 495, 583, 620, 498, 277, 199, 343, 384, 196, 352, 176, 226, 13, 235, 115, 297, 26, 124, 121, 514, 110, 516, 304, 165, 422, 374, 7, 522, 195, 648, 83, 445, 8, 215, 140, 184, 139, 380, 289, 35, 143, 402, 537, 264, 53, 665, 142, 182, 409, 544, 594, 327, 547, 551, 258, 573, 548, 591, 158, 376, 638, 127, 220, 181, 5, 462, 74, 90, 33, 337, 397, 222, 133, 401, 569, 32, 451, 251, 550, 574, 308, 183, 394, 246, 11, 119, 587, 671, 496, 254, 245, 228, 581, 51, 34, 146, 552, 464, 340, 545, 172, 284, 319, 2, 272, 27, 95, 231, 387, 283, 351, 428, 350, 477, 609, 232, 188, 260, 668, 72, 57, 160, 640, 357, 619, 497, 157, 105, 369, 635, 131, 55, 112, 398, 262, 326, 243, 452, 339, 10, 624, 66, 79, 555, 336, 617, 641, 677, 298, 189, 4, 39, 250, 524, 382, 309, 690, 211, 71, 200, 145, 315, 371, 98, 52, 331, 449, 92, 6, 313, 540, 24, 667, 613, 104, 256, 582, 203, 50, 307, 446, 684, 642, 48, 244, 113, 353, 432, 683, 676, 685, 159, 194, 141, 490, 651, 338, 147, 225 ] /* order = 128 = 2^7 */ >; print("a Sylow 2-subgroup of 3.M22");