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[[684,8,85]] d ≤
n
684
k
8
d
85
kd²/n
84.503
w
8

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Distance

d_X 85 · witness weight 85 (claimed upper_bound)
witness operator (support, 85 qubits)
[0, 4, 7, 10, 15, 26, 31, 34, 35, 68, 81, 82, 87, 94, 96, 105, 110, 118, 130, 134, 141, 145, 149, 163, 201, 208, 219, 226, 227, 228, 229, 230, 235, 238, 245, 247, 254, 263, 270, 273, 283, 287, 288, 306, 309, 314, 323, 325, 327, 343, 352, 354, 387, 402, 407, 414, 418, 427, 434, 445, 463, 476, 482, 488, 521, 526, 534, 535, 536, 544, 545, 550, 568, 569, 572, 576, 578, 605, 631, 637, 646, 657, 658, 665, 682]
d_Z 104 · witness weight 104 (claimed upper_bound)
witness operator (support, 104 qubits)
[1, 10, 11, 20, 22, 23, 30, 38, 44, 52, 54, 59, 68, 86, 89, 91, 100, 131, 132, 138, 142, 147, 154, 159, 160, 162, 169, 171, 191, 192, 206, 232, 243, 244, 247, 256, 264, 265, 270, 276, 277, 278, 286, 287, 292, 294, 296, 305, 316, 330, 340, 352, 354, 356, 370, 388, 390, 395, 399, 411, 413, 422, 433, 439, 466, 474, 482, 505, 507, 513, 516, 517, 518, 533, 538, 540, 541, 548, 552, 554, 555, 559, 565, 566, 567, 569, 584, 585, 589, 593, 595, 599, 600, 607, 613, 615, 626, 639, 641, 646, 651, 667, 670, 682]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group algebra (2BGA) over the affine group of F_19: metacyclic(q, q-1, primitive_root) with left-support a=[294, 208, 142, 284] and right-support b=[6, 323, 76, 217]. Built via the research/kit group_algebra build_2bga sampler (sample_kasai_affine, seed=17).
model Tencent Hy3 (claimed, not verified)
builds on arXiv:2601.08824, arXiv:2604.20838
date 2026-07-18
notes Distance is an UPPER BOUND from randomized lightest-logical witness searches. The original d=100 claim (PR #224) was REFUTED by CI: the syndrome-decoder pass found a weight-97 X-logical and the accelerated RIS-fast pass (8M trials) found a weight-85 X-logical, both lighter than 100. This submission corrects the claim to the honest minimum found: d_X <= 85 (RIS-fast witness), d_Z <= 104 (original witness). d = min = 85. Both witnesses are validated against the pinned python stack (gf2.logical_basis / commutes / in_rowspace).
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 342 · Z-checks 342
H_X (342 checks, sparse supports)
[130, 182, 264, 278, 354, 415, 593, 608] [131, 183, 265, 279, 355, 468, 488, 519] [132, 184, 266, 280, 356, 595, 633, 682] [133, 185, 267, 281, 357, 506, 580, 665] [134, 186, 268, 282, 358, 473, 612, 669] [135, 187, 269, 283, 359, 541, 600, 652] [136, 188, 252, 284, 342, 398, 511, 617] [137, 189, 253, 285, 343, 453, 546, 674] [138, 190, 254, 286, 344, 403, 562, 657] [139, 191, 255, 287, 345, 437, 458, 622] [140, 192, 256, 270, 346, 528, 551, 567] [141, 193, 257, 271, 347, 367, 408, 442] [142, 194, 258, 272, 348, 386, 463, 533] [143, 195, 259, 273, 349, 372, 423, 572] [126, 196, 260, 274, 350, 391, 447, 496] [127, 197, 261, 275, 351, 428, 538, 641] [128, 180, 262, 276, 352, 377, 501, 588] [129, 181, 263, 277, 353, 378, 481, 646] [76, 98, 120, 254, 372, 433, 611, 626] [77, 99, 121, 255, 373, 486, 506, 537] [78, 100, 122, 256, 358, 374, 613, 651] [79, 101, 123, 257, 375, 524, 598, 683] [80, 102, 124, 258, 345, 376, 491, 630] [81, 103, 125, 259, 377, 559, 618, 670] [82, 104, 108, 260, 360, 416, 529, 635] [83, 105, 109, 261, 350, 361, 471, 564] [84, 106, 110, 262, 362, 421, 580, 675] [85, 107, 111, 263, 363, 455, 476, 640] [86, 90, 112, 264, 364, 546, 569, 585] [87, 91, 113, 265, 365, 385, 426, 460] [88, 92, 114, 266, 366, 404, 481, 551] [89, 93, 115, 267, 367, 390, 441, 590] [72, 94, 116, 268, 368, 409, 465, 514] [73, 95, 117, 269, 369, 446, 556, 659] [74, 96, 118, 252, 370, 395, 519, 606] [75, 97, 119, 253, 371, 396, 499, 664] [22, 260, 318, 326, 390, 451, 629, 644] [23, 261, 319, 327, 391, 504, 524, 555] [24, 262, 320, 328, 376, 392, 631, 669] [25, 263, 321, 329, 359, 393, 542, 616] [26, 264, 322, 330, 363, 394, 509, 648] [27, 265, 323, 331, 346, 395, 577, 636] [28, 266, 306, 332, 378, 434, 547, 653] [29, 267, 307, 333, 368, 379, 489, 582] [30, 268, 308, 334, 351, 380, 439, 598] [31, 269, 309, 335, 381, 473, 494, 658] [32, 252, 310, 336, 382, 564, 587, 603] [33, 253, 311, 337, 383, 403, 444, 478] [34, 254, 312, 338, 384, 422, 499, 569] [35, 255, 313, 339, 385, 408, 459, 608] [18, 256, 314, 340, 386, 427, 483, 532] [19, 257, 315, 341, 387, 464, 574, 677] [20, 258, 316, 324, 388, 413, 537, 624] [21, 259, 317, 325, 389, 414, 517, 682] [56, 80, 174, 310, 408, 469, 647, 662] [57, 81, 175, 311, 409, 522, 542, 573] [58, 82, 176, 312, 345, 394, 410, 649] [59, 83, 177, 313, 377, 411, 560, 634] [60, 84, 178, 314, 381, 412, 527, 666] [61, 85, 179, 315, 364, 413, 595, 654] [62, 86, 162, 316, 396, 452, 565, 671] [63, 87, 163, 317, 386, 397, 507, 600] [64, 88, 164, 318, 369, 398, 457, 616] [65, 89, 165, 319, 399, 491, 512, 676] [66, 72, 166, 320, 400, 582, 605, 621] [67, 73, 167, 321, 401, 421, 462, 496] [68, 74, 168, 322, 402, 440, 517, 587] [69, 75, 169, 323, 403, 426, 477, 626] [70, 76, 170, 306, 404, 445, 501, 550] [71, 77, 171, 307, 353, 405, 482, 592] [54, 78, 172, 308, 406, 431, 555, 642] [55, 79, 173, 309, 358, 407, 432, 535] [30, 128, 242, 256, 426, 487, 665, 680] [31, 129, 243, 257, 427, 540, 560, 591] [32, 130, 244, 258, 363, 412, 428, 667] [33, 131, 245, 259, 395, 429, 578, 652] [34, 132, 246, 260, 342, 399, 430, 545] [35, 133, 247, 261, 382, 431, 613, 672] [18, 134, 248, 262, 347, 414, 470, 583] [19, 135, 249, 263, 404, 415, 525, 618] [20, 136, 250, 264, 387, 416, 475, 634] [21, 137, 251, 265, 352, 417, 509, 530] [22, 138, 234, 266, 418, 600, 623, 639] [23, 139, 235, 267, 419, 439, 480, 514] [24, 140, 236, 268, 420, 458, 535, 605] [25, 141, 237, 269, 421, 444, 495, 644] [26, 142, 238, 252, 422, 463, 519, 568] [27, 143, 239, 253, 371, 423, 500, 610] [28, 126, 240, 254, 424, 449, 573, 660] [29, 127, 241, 255, 376, 425, 450, 553] [62, 200, 202, 228, 356, 444, 505, 683] [63, 201, 203, 229, 445, 558, 578, 609] [64, 202, 204, 230, 343, 381, 430, 446] [65, 203, 205, 231, 413, 447, 596, 670] [66, 204, 206, 232, 360, 417, 448, 563] [67, 205, 207, 233, 348, 400, 449, 631] [68, 206, 208, 216, 365, 432, 488, 601] [69, 207, 209, 217, 422, 433, 543, 636] [70, 208, 210, 218, 405, 434, 493, 652] [71, 209, 211, 219, 370, 435, 527, 548] [54, 210, 212, 220, 436, 618, 641, 657] [55, 211, 213, 221, 437, 457, 498, 532] [56, 212, 214, 222, 438, 476, 553, 623] [57, 213, 215, 223, 439, 462, 513, 662] [58, 198, 214, 224, 440, 481, 537, 586] [59, 199, 215, 225, 389, 441, 518, 628] [60, 198, 200, 226, 442, 467, 591, 678] [61, 199, 201, 227, 394, 443, 468, 571] [84, 148, 224, 272, 359, 374, 462, 523] [85, 149, 225, 273, 463, 576, 596, 627] [86, 150, 226, 274, 361, 399, 448, 464] [87, 151, 227, 275, 346, 431, 465, 614] [88, 152, 228, 276, 378, 435, 466, 581] [89, 153, 229, 277, 366, 418, 467, 649] [72, 154, 230, 278, 383, 450, 506, 619] [73, 155, 231, 279, 440, 451, 561, 654] [74, 156, 232, 280, 423, 452, 511, 670] [75, 157, 233, 281, 388, 453, 545, 566] [76, 158, 216, 282, 454, 636, 659, 675] [77, 159, 217, 283, 455, 475, 516, 550] [78, 160, 218, 284, 456, 494, 571, 641] [79, 161, 219, 285, 457, 480, 531, 680] [80, 144, 220, 286, 458, 499, 555, 604] [81, 145, 221, 287, 407, 459, 536, 646] [82, 146, 222, 270, 354, 460, 485, 609] [83, 147, 223, 271, 412, 461, 486, 589] [2, 44, 94, 282, 377, 392, 480, 541] [3, 45, 95, 283, 481, 594, 614, 645] [4, 46, 96, 284, 379, 417, 466, 482] [5, 47, 97, 285, 364, 449, 483, 632] [6, 48, 98, 286, 396, 453, 484, 599] [7, 49, 99, 287, 384, 436, 485, 667] [8, 50, 100, 270, 401, 468, 524, 637] [9, 51, 101, 271, 458, 469, 579, 672] [10, 52, 102, 272, 346, 441, 470, 529] [11, 53, 103, 273, 406, 471, 563, 584] [12, 36, 104, 274, 351, 472, 654, 677] [13, 37, 105, 275, 473, 493, 534, 568] [14, 38, 106, 276, 474, 512, 589, 659] [15, 39, 107, 277, 356, 475, 498, 549] [16, 40, 90, 278, 476, 517, 573, 622] [17, 41, 91, 279, 425, 477, 554, 664] [0, 42, 92, 280, 372, 478, 503, 627] [1, 43, 93, 281, 430, 479, 504, 607] [40, 74, 138, 206, 395, 410, 498, 559] [41, 75, 139, 207, 499, 612, 632, 663] [42, 76, 140, 208, 397, 435, 484, 500] [43, 77, 141, 209, 382, 467, 501, 650] [44, 78, 142, 210, 414, 471, 502, 617] [45, 79, 143, 211, 343, 402, 454, 503] [46, 80, 126, 212, 419, 486, 542, 655] [47, 81, 127, 213, 348, 476, 487, 597] [48, 82, 128, 214, 364, 459, 488, 547] [49, 83, 129, 215, 424, 489, 581, 602] [50, 84, 130, 198, 353, 369, 490, 672] [51, 85, 131, 199, 491, 511, 552, 586] [52, 86, 132, 200, 492, 530, 607, 677] [53, 87, 133, 201, 374, 493, 516, 567] [36, 88, 134, 202, 494, 535, 591, 640] [37, 89, 135, 203, 443, 495, 572, 682] [38, 72, 136, 204, 390, 496, 521, 645] [39, 73, 137, 205, 448, 497, 522, 625] [26, 146, 328, 336, 413, 428, 516, 577] [27, 147, 329, 337, 517, 630, 650, 681] [28, 148, 330, 338, 415, 453, 502, 518] [29, 149, 331, 339, 400, 485, 519, 668] [30, 150, 332, 340, 432, 489, 520, 635] [31, 151, 333, 341, 361, 420, 472, 521] [32, 152, 324, 334, 437, 504, 560, 673] [33, 153, 325, 335, 366, 494, 505, 615] [34, 154, 326, 336, 382, 477, 506, 565] [35, 155, 327, 337, 442, 507, 599, 620] [18, 156, 328, 338, 348, 371, 387, 508] [19, 157, 329, 339, 509, 529, 570, 604] [20, 158, 330, 340, 353, 510, 548, 625] [21, 159, 331, 341, 392, 511, 534, 585] [22, 160, 324, 332, 512, 553, 609, 658] [23, 161, 325, 333, 358, 461, 513, 590] [24, 144, 326, 334, 408, 514, 539, 663] [25, 145, 327, 335, 466, 515, 540, 643] [188, 192, 218, 274, 431, 446, 534, 595] [189, 193, 219, 275, 357, 535, 648, 668] [190, 194, 220, 276, 433, 471, 520, 536] [191, 195, 221, 277, 344, 418, 503, 537] [192, 196, 222, 278, 450, 507, 538, 653] [193, 197, 223, 279, 379, 438, 490, 539] [180, 194, 224, 280, 349, 455, 522, 578] [181, 195, 225, 281, 384, 512, 523, 633] [182, 196, 226, 282, 400, 495, 524, 583] [183, 197, 227, 283, 460, 525, 617, 638] [180, 184, 228, 284, 366, 389, 405, 526] [181, 185, 229, 285, 527, 547, 588, 622] [182, 186, 230, 286, 371, 528, 566, 643] [183, 187, 231, 287, 410, 529, 552, 603] [184, 188, 232, 270, 530, 571, 627, 676] [185, 189, 233, 271, 376, 479, 531, 608] [186, 190, 216, 272, 426, 532, 557, 681] [187, 191, 217, 273, 484, 533, 558, 661] [8, 48, 220, 290, 449, 464, 552, 613] [9, 49, 221, 291, 344, 375, 553, 666] [10, 50, 222, 292, 451, 489, 538, 554] [11, 51, 223, 293, 362, 436, 521, 555] [12, 52, 224, 294, 468, 525, 556, 671] [13, 53, 225, 295, 397, 456, 508, 557] [14, 36, 226, 296, 367, 473, 540, 596] [15, 37, 227, 297, 402, 530, 541, 651] [16, 38, 228, 298, 418, 513, 542, 601] [17, 39, 229, 299, 478, 543, 635, 656] [0, 40, 230, 300, 384, 407, 423, 544] [1, 41, 231, 301, 545, 565, 606, 640] [2, 42, 232, 302, 389, 546, 584, 661] [3, 43, 233, 303, 428, 547, 570, 621] [4, 44, 216, 304, 352, 548, 589, 645] [5, 45, 217, 305, 394, 497, 549, 626] [6, 46, 218, 288, 357, 444, 550, 575] [7, 47, 219, 289, 502, 551, 576, 679] [20, 166, 170, 246, 467, 482, 570, 631] [21, 167, 171, 247, 342, 362, 393, 571] [22, 168, 172, 248, 469, 507, 556, 572] [23, 169, 173, 249, 380, 454, 539, 573] [24, 170, 174, 250, 347, 486, 543, 574] [25, 171, 175, 251, 415, 474, 526, 575] [26, 172, 176, 234, 385, 491, 558, 614] [27, 173, 177, 235, 420, 548, 559, 669] [28, 174, 178, 236, 436, 531, 560, 619] [29, 175, 179, 237, 496, 561, 653, 674] [30, 162, 176, 238, 402, 425, 441, 562] [31, 163, 177, 239, 563, 583, 624, 658] [32, 164, 178, 240, 407, 564, 602, 679] [33, 165, 179, 241, 446, 565, 588, 639] [34, 162, 166, 242, 370, 566, 607, 663] [35, 163, 167, 243, 412, 515, 567, 644] [18, 164, 168, 244, 375, 462, 568, 593] [19, 165, 169, 245, 355, 520, 569, 594] [92, 102, 112, 332, 485, 500, 588, 649] [93, 103, 113, 333, 360, 380, 411, 589] [94, 104, 114, 334, 487, 525, 574, 590] [95, 105, 115, 335, 398, 472, 557, 591] [96, 106, 116, 336, 365, 504, 561, 592] [97, 107, 117, 337, 433, 492, 544, 593] [90, 98, 118, 338, 403, 509, 576, 632] [91, 99, 119, 339, 345, 438, 566, 577] [92, 100, 120, 340, 454, 549, 578, 637] [93, 101, 121, 341, 350, 514, 579, 671] [94, 102, 122, 324, 420, 443, 459, 580] [95, 103, 123, 325, 581, 601, 642, 676] [96, 104, 124, 326, 355, 425, 582, 620] [97, 105, 125, 327, 464, 583, 606, 657] [98, 106, 108, 328, 388, 584, 625, 681] [99, 107, 109, 329, 430, 533, 585, 662] [90, 100, 110, 330, 393, 480, 586, 611] [91, 101, 111, 331, 373, 538, 587, 612] [58, 152, 164, 300, 503, 518, 606, 667] [59, 153, 165, 301, 378, 398, 429, 607] [60, 154, 166, 302, 505, 543, 592, 608] [61, 155, 167, 303, 416, 490, 575, 609] [62, 156, 168, 304, 383, 522, 579, 610] [63, 157, 169, 305, 451, 510, 562, 611] [64, 158, 170, 288, 421, 527, 594, 650] [65, 159, 171, 289, 363, 456, 584, 595] [66, 160, 172, 290, 472, 567, 596, 655] [67, 161, 173, 291, 347, 368, 532, 597] [68, 144, 174, 292, 438, 461, 477, 598] [69, 145, 175, 293, 352, 599, 619, 660] [70, 146, 176, 294, 373, 443, 600, 638] [71, 147, 177, 295, 482, 601, 624, 675] [54, 148, 178, 296, 357, 406, 602, 643] [55, 149, 179, 297, 448, 551, 603, 680] [56, 150, 162, 298, 411, 498, 604, 629] [57, 151, 163, 299, 391, 556, 605, 630] [4, 156, 236, 314, 343, 521, 536, 624] [5, 157, 237, 315, 396, 416, 447, 625] [6, 158, 238, 316, 523, 561, 610, 626] [7, 159, 239, 317, 434, 508, 593, 627] [8, 160, 240, 318, 401, 540, 597, 628] [9, 161, 241, 319, 469, 528, 580, 629] [10, 144, 242, 320, 439, 545, 612, 668] [11, 145, 243, 321, 381, 474, 602, 613] [12, 146, 244, 322, 490, 585, 614, 673] [13, 147, 245, 323, 365, 386, 550, 615] [14, 148, 246, 306, 456, 479, 495, 616] [15, 149, 247, 307, 370, 617, 637, 678] [16, 150, 248, 308, 391, 461, 618, 656] [17, 151, 249, 309, 351, 500, 619, 642] [0, 152, 250, 310, 375, 424, 620, 661] [1, 153, 251, 311, 356, 466, 569, 621] [2, 154, 234, 312, 429, 516, 622, 647] [3, 155, 235, 313, 409, 574, 623, 648] [12, 134, 292, 308, 361, 539, 554, 642] [13, 135, 293, 309, 414, 434, 465, 643] [14, 136, 294, 310, 541, 579, 628, 644] [15, 137, 295, 311, 452, 526, 611, 645] [16, 138, 296, 312, 419, 558, 615, 646] [17, 139, 297, 313, 487, 546, 598, 647] [0, 140, 298, 314, 344, 457, 563, 630] [1, 141, 299, 315, 399, 492, 620, 631] [2, 142, 300, 316, 349, 508, 603, 632] [3, 143, 301, 317, 383, 404, 568, 633] [4, 126, 302, 318, 474, 497, 513, 634] [5, 127, 303, 319, 354, 388, 635, 655] [6, 128, 304, 320, 409, 479, 636, 674] [7, 129, 305, 321, 369, 518, 637, 660] [8, 130, 288, 322, 393, 442, 638, 679] [9, 131, 289, 323, 374, 484, 587, 639] [10, 132, 290, 306, 447, 534, 640, 665] [11, 133, 291, 307, 427, 592, 641, 666] [38, 210, 238, 296, 379, 557, 572, 660] [39, 211, 239, 297, 432, 452, 483, 661] [40, 212, 240, 298, 559, 597, 646, 662] [41, 213, 241, 299, 470, 544, 629, 663] [42, 214, 242, 300, 437, 576, 633, 664] [43, 215, 243, 301, 505, 564, 616, 665] [44, 198, 244, 302, 362, 475, 581, 648] [45, 199, 245, 303, 417, 510, 638, 649] [46, 200, 246, 304, 367, 526, 621, 650] [47, 201, 247, 305, 401, 422, 586, 651] [48, 202, 248, 288, 492, 515, 531, 652] [49, 203, 249, 289, 372, 406, 653, 673] [50, 204, 250, 290, 350, 427, 497, 654] [51, 205, 251, 291, 387, 536, 655, 678] [52, 206, 234, 292, 355, 411, 460, 656] [53, 207, 235, 293, 392, 502, 605, 657] [36, 208, 236, 294, 465, 552, 658, 683] [37, 209, 237, 295, 342, 445, 610, 659] [66, 110, 116, 184, 397, 575, 590, 678] [67, 111, 117, 185, 450, 470, 501, 679] [68, 112, 118, 186, 577, 615, 664, 680] [69, 113, 119, 187, 488, 562, 647, 681] [70, 114, 120, 188, 455, 594, 651, 682] [71, 115, 121, 189, 523, 582, 634, 683] [54, 116, 122, 190, 380, 493, 599, 666] [55, 117, 123, 191, 435, 528, 656, 667] [56, 118, 124, 192, 385, 544, 639, 668] [57, 119, 125, 193, 419, 440, 604, 669] [58, 108, 120, 194, 510, 533, 549, 670] [59, 109, 121, 195, 349, 390, 424, 671] [60, 110, 122, 196, 368, 445, 515, 672] [61, 111, 123, 197, 354, 405, 554, 673] [62, 112, 124, 180, 373, 429, 478, 674] [63, 113, 125, 181, 410, 520, 623, 675] [64, 108, 114, 182, 359, 483, 570, 676] [65, 109, 115, 183, 360, 463, 628, 677]
H_Z (342 checks, sparse supports)
[6, 76, 217, 323, 484, 550, 626, 636] [7, 92, 149, 270, 485, 551, 627, 637] [8, 183, 199, 294, 468, 552, 628, 638] [9, 22, 56, 241, 469, 553, 629, 639] [10, 41, 111, 134, 470, 554, 612, 640] [11, 78, 220, 261, 471, 555, 613, 641] [12, 95, 151, 172, 472, 556, 614, 642] [13, 186, 296, 335, 473, 557, 615, 643] [14, 25, 243, 318, 474, 540, 616, 644] [15, 44, 136, 283, 475, 541, 617, 645] [16, 81, 212, 263, 476, 542, 618, 646] [17, 69, 154, 174, 477, 543, 619, 647] [0, 124, 299, 337, 478, 544, 620, 630] [1, 233, 246, 320, 479, 545, 621, 631] [2, 90, 139, 285, 480, 546, 622, 632] [3, 181, 214, 266, 481, 547, 623, 633] [4, 20, 71, 177, 482, 548, 624, 634] [5, 39, 108, 340, 483, 549, 625, 635] [24, 94, 235, 341, 392, 420, 514, 574] [25, 110, 167, 288, 393, 421, 515, 575] [26, 201, 217, 312, 394, 422, 516, 558] [27, 40, 74, 259, 395, 423, 517, 559] [28, 59, 129, 152, 378, 424, 518, 560] [29, 96, 238, 279, 379, 425, 519, 561] [30, 113, 169, 190, 380, 426, 520, 562] [11, 31, 204, 314, 381, 427, 521, 563] [32, 43, 261, 336, 382, 428, 504, 564] [33, 62, 154, 301, 383, 429, 505, 565] [34, 99, 230, 281, 384, 430, 506, 566] [35, 87, 172, 192, 385, 431, 507, 567] [13, 18, 142, 317, 386, 414, 508, 568] [19, 251, 264, 338, 387, 415, 509, 569] [20, 108, 157, 303, 388, 416, 510, 570] [21, 199, 232, 284, 389, 417, 511, 571] [22, 38, 89, 195, 390, 418, 512, 572] [16, 23, 57, 126, 391, 419, 513, 573] [17, 42, 112, 253, 478, 500, 546, 664] [43, 128, 185, 306, 479, 501, 547, 665] [44, 219, 235, 330, 480, 502, 548, 648] [45, 58, 92, 277, 481, 503, 549, 649] [46, 77, 147, 170, 482, 486, 550, 650] [47, 114, 256, 297, 483, 487, 551, 651] [48, 131, 187, 208, 484, 488, 552, 652] [29, 49, 222, 332, 485, 489, 553, 653] [12, 50, 61, 279, 468, 490, 554, 654] [51, 80, 172, 319, 469, 491, 555, 655] [52, 117, 248, 299, 470, 492, 556, 656] [53, 105, 190, 210, 471, 493, 557, 657] [31, 36, 160, 335, 472, 494, 540, 658] [14, 37, 269, 282, 473, 495, 541, 659] [38, 126, 175, 321, 474, 496, 542, 660] [39, 217, 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raw submission JSON