[[682,140,82]] · QEC Challenge

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[[682,140,82]] d ≤

682

140

kd²/n

1380.293

X/Z

1.02

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Distance

X/Z asymmetry 1.02 · d_X ≤ 82, d_Z ≤ 84 · w_X = 30, w_Z = 30 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 82 · witness weight 82 (claimed upper_bound)

witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×10⁸ trials · survived 3×10⁸ trials · 2026-09-24

witness operator (support, 82 qubits)

[0, 3, 4, 6, 12, 14, 17, 24, 32, 33, 40, 48, 57, 60, 64, 67, 68, 71, 72, 74, 76, 79, 80, 81, 83, 84, 95, 109, 111, 112, 114, 117, 133, 139, 141, 144, 145, 158, 159, 165, 174, 175, 176, 182, 187, 189, 193, 194, 196, 203, 204, 207, 213, 216, 218, 220, 224, 235, 240, 247, 250, 258, 264, 269, 277, 285, 302, 343, 354, 355, 364, 375, 416, 418, 424, 457, 558, 562, 576, 601, 658, 663]

d_Z 84 · witness weight 84 (claimed upper_bound)

witness found by @DennisWayo · GB involution mirror of gf2_fast structural witness · found at 4×10⁵ trials · survived 8×10⁶ trials · 2026-09-22

witness operator (support, 84 qubits)

[353, 354, 355, 356, 358, 366, 374, 376, 378, 380, 386, 391, 398, 399, 400, 405, 407, 409, 410, 412, 413, 414, 415, 422, 430, 438, 440, 447, 448, 452, 454, 455, 456, 465, 467, 469, 471, 473, 474, 479, 485, 490, 491, 492, 498, 502, 504, 506, 511, 514, 518, 520, 523, 528, 533, 534, 536, 537, 547, 550, 552, 555, 559, 575, 577, 578, 580, 581, 589, 597, 598, 605, 606, 608, 610, 622, 630, 636, 642, 644, 645, 653, 662, 668]

certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 30 · H_Z 30

qubit degrees H_X 15 · H_Z 15

trapping sets H_X (1,15)×682 (2,18)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)

full (size, syndrome weight): count census for H_X

(1,15): 682 (2,18): 341 (2,22): 2387 (2,24): 4774 (2,26): 24211 (2,28): 73997

trapping sets H_Z (1,15)×682 (2,18)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)

full (size, syndrome weight): count census for H_Z

(1,15): 682 (2,18): 341 (2,22): 2387 (2,24): 4774 (2,26): 24211 (2,28): 73997

Construction & provenance

authors @DennisWayo

provenance submitted through the challenge

novelty novelty not audited

construction Cyclic generalized-bicycle code over Z_341; a=[0, 7, 22, 41, 51, 95, 114, 165, 176, 198, 224, 238, 268, 289, 312]; b=[8, 66, 80, 96, 105, 115, 178, 192, 205, 221, 256, 279, 280, 293, 324]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].

model OpenAI GPT-5 (Codex) (claimed, not verified)

date 2026-09-22

notes Recovered from a collapsed-candidate bank and retained by a live-board Pareto filter on (n,k,d,max check weight). A 400000-trial circulant-GB structural search found the submitted X witness; the Z witness is its independently verified GB block-swap/index-reversal image. A final local CI-style pass at d<=84 completed another 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 84; RIS-fast stopped at weight 86. Base-board validation reports no exact or WL duplicate. The current codes/682-140-82.json entry has d<=82 and maximum check weight 30; this distinct representation raises the witnessed distance to 84 at the same maximum check weight and scores 1448.446. This is an upper-bound claim, not an exact-distance certificate.

family generalized bicycle (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[682,140,82]]: distance revision of the board's [[682,140,84]] entry

Revision history

[[682,140,82]] supersedes the board's [[682,140,84]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4101) exhibits a weight-82 X logical, so the previous witness-backed bound was overstated and the honest parameter set is [[682,140,82]]. The headline falls from kd^2/n = 1448.45 to 1380.29. Each lighter witness is carried in the entry with the budget it was found at; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 84 | 82 | 82 | 300,000,000 | | Z | 4101 | 84 | 86 | 86 | 300,000,000 | | X | 4102 | 84 | 84 | 84 | 300,000,000 | | Z | 4102 | 84 | 84 | 84 | 300,000,000 |

Original note, with the file paths updated

[[682,140,84]] - weight-30 cyclic generalized-bicycle representation

Direction & hypothesis

This continuation search targeted the unrestricted, weight-9plus cell below the challenge's n <= 700 limit. The hypothesis was that the collapsed cyclic-GB bank contained additional high-distance representatives after the first frontier batch and its submitted fingerprints were removed.

The current codes/682-140-82.json entry has effective parameters [[682,140,d<=82]] and maximum check weight 30. This submission raises the witnessed distance to 84 at the same maximum check weight. Its scalar score is 1448.446. The trusted validator finds neither an exact fingerprint duplicate nor a matching WL signature on the base board.

What was searched

The continuation filter revisited 6,842 reconstructed cyclic-GB records after excluding the 12 fingerprints completed in the first fire batch. Of the 6,794 valid records, 4,999 were already dominated by the projected board. The remaining 1,783 records formed five frontier tuples, from which four representatives per tuple were selected.

The final fire set contained four [[682,140,d<=85]], w=31 and four [[682,140,d<=84]], w=30 representatives. All four d84 representatives share one WL signature. The submitted representative was selected because its 8M RIS-fast pass stayed at weight 86. Two alternatives survived only at the claim boundary of 84, while the fourth was refuted at weight 82.

Evidence trail

The submitted X witness has weight 84. Its Z witness is the weight-preserving generalized-bicycle involution image obtained by swapping the two circulant blocks and reversing their indices. Both witnesses were independently checked for commutation and nontriviality by the trusted GF(2) verifier.

| Stage | Seed | Budget | Outcome | |---|---:|---:|---| | Source circulant-GB structural screen | 158395771496412633 | 400,000 | found submitted weight-84 X witness | | Final circulant-GB gate | 9220011 | 400,000 | no refutation; weight 84 | | Final Python RIS gate | 9220000 | 106,840, 240 s cap | no refutation; best sampled weight 90 | | Final RIS-fast gate | 9220007 | 8,000,000 | no refutation; best sampled weight 86 |

The final uninterrupted gate took about 47.5 minutes locally. The claim remains a witness-backed upper bound d <= 84, not an exact-distance certificate. Hosted CI uses a fresh seed and may still find a lighter logical.

Dead ends

The continuation batch skipped four packaged d80 candidates that were WL-equivalent to a merged board entry. Within the d84 group, the refuted representative demonstrates why a structural witness and short Python RIS pass are insufficient by themselves. Only one representative per WL group is promoted, and the longest independent pass determines the choice.

Tools

Coordinating model: OpenAI GPT-5 (Codex), matching provenance.model. The workflow used a cyclic-ideal generalized-bicycle miner, exact GF(2) rank and commutation checks, a live-board Pareto filter, the trusted circulant-GB structural gate, Python RIS, and the native gf2_fast refuter. Model attribution is self-reported; the public verifier performs all mathematical acceptance checks.

Reproduction

Let C(S) be the 341 by 341 binary circulant whose row i has ones at columns (i+s) mod 341 for s in S. Use H_X = [C(A) | C(B)] and H_Z = [C(B)^T | C(A)^T], with

A = [0,7,22,41,51,95,114,165,176,198,224,238,268,289,312]
B = [8,66,80,96,105,115,178,192,205,221,256,279,280,293,324]

The following standard-library-only snippet reconstructs the submitted rows:

import json
from pathlib import Path

m = 341
A = [0,7,22,41,51,95,114,165,176,198,224,238,268,289,312]
B = [8,66,80,96,105,115,178,192,205,221,256,279,280,293,324]
hx = [sorted([(i+a) % m for a in A] +
             [m+(i+b) % m for b in B]) for i in range(m)]
hz = [sorted([(i-b) % m for b in B] +
             [m+(i-a) % m for a in A]) for i in range(m)]
doc = json.loads(Path("codes/682-140-82-b.json").read_text())
assert doc["checks"]["X"] == hx
assert doc["checks"]["Z"] == hz

Verify the schema, CSS relations, ranks, check weight, and both logical witnesses from the repository root:

uv run --frozen python verify/qldpc_verify.py codes/682-140-82-b.json

Parity checks

X-checks 341 (max weight 30) · Z-checks 341 (max weight 30)

H_X (341 checks, sparse supports)

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

H_Z (341 checks, sparse supports)

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