[[682,140,66]] · QEC Challenge

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[[682,140,66]] d ≤

682

140

kd²/n

894.194

X/Z

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Distance

X/Z asymmetry 1 · d_X ≤ 66, d_Z ≤ 66 · w_X = 31, w_Z = 31 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 66 · witness weight 66 (claimed upper_bound)

witness found by @VedantMahadik-qc · norm-word lift of a Z_31 quotient logical (exact algebra) · found at 1 trials · survived 1 trials · 2026-09-26

witness operator (support, 66 qubits)

[12, 29, 43, 60, 74, 91, 105, 122, 136, 153, 167, 184, 198, 215, 229, 246, 260, 277, 291, 308, 322, 339, 341, 346, 350, 355, 372, 377, 381, 386, 403, 408, 412, 417, 434, 439, 443, 448, 465, 470, 474, 479, 496, 501, 505, 510, 527, 532, 536, 541, 558, 563, 567, 572, 589, 594, 598, 603, 620, 625, 629, 634, 651, 656, 660, 665]

d_Z 66 · witness weight 66 (claimed upper_bound)

witness found by @VedantMahadik-qc · norm-word lift of a Z_31 quotient logical (exact algebra) · found at 1 trials · survived 1 trials · 2026-09-26

witness operator (support, 66 qubits)

[3, 7, 12, 29, 34, 38, 43, 60, 65, 69, 74, 91, 96, 100, 105, 122, 127, 131, 136, 153, 158, 162, 167, 184, 189, 193, 198, 215, 220, 224, 229, 246, 251, 255, 260, 277, 282, 286, 291, 308, 313, 317, 322, 339, 341, 355, 372, 386, 403, 417, 434, 448, 465, 479, 496, 510, 527, 541, 558, 572, 589, 603, 620, 634, 651, 665]

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 31 · H_Z 31

qubit degrees H_X 15–16 (mean 15.5) · H_Z 15–16 (mean 15.5)

trapping sets H_X (1,15)×341 (2,21)×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): 341 (1,16): 341 (2,21): 341 (2,23): 341 (2,24): 2046 (2,25): 2387 (2,26): 5797 (2,27): 15004 (2,28): 30349 (2,29): 41602 (2,30): 18073

trapping sets H_Z (1,15)×341 (2,21)×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): 341 (1,16): 341 (2,21): 341 (2,23): 341 (2,24): 2046 (2,25): 2387 (2,26): 5797 (2,27): 15004 (2,28): 30349 (2,29): 41602 (2,30): 18073

Construction & provenance

authors @DennisWayo

provenance submitted through the challenge

novelty novelty not audited

construction Cyclic generalized-bicycle code over Z_341; a=[0, 1, 4, 27, 53, 79, 99, 137, 162, 223, 225, 294, 323, 331, 334]; b=[2, 122, 124, 131, 132, 134, 137, 168, 207, 220, 241, 268, 296, 297, 303, 308]; 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<=85 completed another 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 85; 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 85 at maximum check weight 31 and scores 1483.138. This is an upper-bound claim, not an exact-distance certificate. Tightened 2026-09-22 by @vprusso: a GPU random-information-set search (verify/ris_gpu.py, recover mode, k_sub 128, 80,000,000 trials per side, seed 1003) exhibits a weight-83 Z-type logical, so d <= 83; weight-84 X-type logicals were found at seeds 1002 (k_sub 64) and 1003 (k_sub 128), and 260,000,000 sketch trials per side over k_sub 32, 64, 128, and 256 plus 4,000,000 deep-kernel trials found nothing lighter than 83. The X witness is the original weight-85 operator, since the weight-84 X operators only lower a side value, not d. Every GPU operator was re-verified on the CPU with verify/gf2.py. Tightened 2026-09-26 by @VedantMahadik-qc: the Z_31 quotient code (both generator polynomials reduced modulo x^31 - 1) has a weight-6 logical on each side, and its norm-word lift (multiplication by 1 + x^31 + ... + x^310) is a weight-66 logical of the full code, so d <= 66. The code, checks, and authorship are unchanged; only the distance block and name are revised.

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

[[682,140,66]]: distance revision of the board's [[682,140,83]] entry

Revision history

[[682,140,66]] supersedes the board's [[682,140,83]] entry. The code, its checks, and its original provenance are unchanged; only the distance block and the name are corrected. The entry is a cyclic generalized-bicycle code on Z_341 with H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T]. Structural witnesses exhibit a weight-66 X logical and a weight-66 Z logical: on both sides, the Z_31 quotient code (both generator polynomials reduced modulo x^31 - 1, quotient dimension 20) has a weight-6 logical whose norm-word lift, multiplication by 1 + x^31 + ... + x^310 (11 terms), is a weight-66 logical of the full code. The X claim falls from 85 to 66 and the Z claim from 83 to 66, so d falls from 83 to 66. Efficiency k d^2 / n falls from 1414.2 to 894.3. Distance remains an upper bound, not an exact claim.

Evidence

The witnesses are not sampled on the full code. A quotient logical is found by information-set search on the small quotient code, lifted by the norm word (which maps the kernel of the quotient Z checks into the kernel of the full Z checks and cannot turn a non-stabilizer into a stabilizer, since the norm word is 1 modulo x^31 - 1), and re-validated on the committed check matrices: in the kernel of the opposite side's checks and outside the row space of its own side. The witness_provenance sampling fields therefore carry the placeholder 1 and the tool field names the construction. Running uv run --frozen python verify/qldpc_verify.py codes/682-140-66.json confirms, for each side, weight 66, membership in the kernel, and nontriviality, and reports d as the minimum of the two sides.

| side | claimed | lightest witness | mechanism | |---|---|---|---| | X | 85 | 66 | quotient m'=31, 1,500 trials over seeds 0, 1, 2 | | Z | 83 | 66 | quotient m'=31, 1,500 trials over seeds 0, 1, 2 |

Quotient search log (information-set search on the Z_31 quotient code, k_q = 20):

| m' | k of quotient | side | quotient weight | lifted weight | lift valid | |---|---|---|---|---|---| | 31 | 20 | X | 6 | 66 | yes | | 31 | 20 | Z | 6 | 66 | yes |

The earlier RIS passes on this entry (8,000,000 RIS-fast trials, and 260,000,000 GPU sketch trials per side, recorded below) did not find these operators; they sit in the low-dimensional subspace of norm-word multiples that a plain information-set search rarely samples. The audit method is described in fieldnotes/2026-09-22-frontier-truth-gpu-audit.md.

Original note, with the file paths updated

[[682,140,83]] - weight-31 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 85 at maximum check weight 31. Its scalar score is 1483.138, above the pre-submission board maximum of 1456.704. 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 first continuation package contained four [[682,140,d<=85]], w=31, four [[682,140,d<=84]], w=30, and four [[682,142,d<=80]], w=24 representatives. The last group was not fired because it was WL-equivalent to an existing board entry. All four d85 representatives share one WL signature. The submitted representative was selected because its 8M RIS-fast pass stayed at weight 86. One alternative survived only at the claim boundary of 85, and the other two were refuted at weights 84 and 82.

Evidence trail

The submitted X witness has weight 85. 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 | 941253214970200228 | 400,000 | found submitted weight-85 X witness | | Final circulant-GB gate | 9220011 | 400,000 | no refutation; weight 85 | | Final Python RIS gate | 9220000 | 106,840, 240 s cap | no refutation; best sampled weight 93 | | 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 <= 85, not an exact-distance certificate. Hosted CI uses a fresh seed and may still find a lighter logical.

Dead ends

The continuation batch deliberately skipped four packaged d80 candidates that were WL-equivalent to a merged board entry. Within the d85 group, the two refuted representatives demonstrate 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 = [0,1,4,27,53,79,99,137,162,223,225,294,323,331,334]
B = [2,122,124,131,132,134,137,168,207,220,241,268,296,297,303,308]

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

import json
from pathlib import Path

m = 341
A = [0,1,4,27,53,79,99,137,162,223,225,294,323,331,334]
B = [2,122,124,131,132,134,137,168,207,220,241,268,296,297,303,308]
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/682-140-66.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/682-140-66.json

Tightening (2026-09-22)

The Z-side claim of 85 did not hold. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 128-row sketch, 80,000,000 trials per side, seed 1003, one NVIDIA A40) found a Z-type logical of weight 83; the submission's own 8,000,000-trial RIS-fast pass and 400,000-trial structural pass stopped at weight 86, which is why the original claim passed the gate. The weight-83 operator was re-verified on the CPU with verify/gf2.py (zero syndrome against H_X, outside the row space of H_Z, weight recounted) and is embedded as the Z-side witness with its witness_provenance. The X side keeps its original weight-85 witness: weight-84 X-type logicals exist (table below) but do not lower d. The file was renamed to d = 83 (distance.d = 83), and the claim stays a witnessed upper bound.

Every GPU proposal was re-validated on the CPU with verify/gf2.py before it was recorded.

| side | claimed | lightest logical found | sketch rows (k_sub) | trials per side | seed | |---|---:|---:|---:|---:|---:| | X | 85 | 88 | 32 | 80,000,000 | 1001 | | Z | 85 | 87 | 32 | 80,000,000 | 1001 | | X | 85 | 84 | 64 | 80,000,000 | 1002 | | Z | 85 | 86 | 64 | 80,000,000 | 1002 | | X | 85 | 84 | 128 | 80,000,000 | 1003 | | Z | 85 | 83 | 128 | 80,000,000 | 1003 | | X | 85 | 86 | 256 | 20,000,000 | 1005 | | Z | 85 | 84 | 256 | 20,000,000 | 1005 | | X | 85 | 89 | deep kernel, pair depth 8 | 4,000,000 | 1004 | | Z | 85 | 86 | deep kernel, pair depth 8 | 4,000,000 | 1004 |

In total 260,000,000 sketch trials and 4,000,000 deep-kernel trials per side, about 1.5 GPU hours; nothing lighter than 83 appeared. Efficiency k d^2 / n = 140 * 83^2 / 682 = 1414.2, down from 1483.1. At d = 83 with check weight 31 the entry was dominated at (682, 140) by a then-current d 84, check weight 30 entry. The sections above describe the original submission and are left as the record of what was claimed.

Parity checks

X-checks 341 (max weight 31) · Z-checks 341 (max weight 31)

H_X (341 checks, sparse supports)

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

H_Z (341 checks, sparse supports)

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