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[[682,172,72]] d ≤
n
682
k
172
d
72
kd²/n
1307.402
w
32
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 72, d_Z ≤ 72 · w_X = 32, w_Z = 32 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 72 · witness weight 72 (claimed upper_bound)
witness found by @vprusso · single-block logical from the constituent cyclic code (exact, not sampled) · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 72 qubits)
[10, 17, 19, 20, 31, 38, 41, 52, 59, 70, 72, 79, 91, 92, 101, 102, 103, 105, 110, 113, 132, 134, 138, 148, 149, 152, 153, 162, 163, 164, 165, 168, 171, 172, 175, 185, 191, 192, 196, 201, 202, 222, 227, 230, 233, 235, 236, 246, 253, 258, 260, 263, 264, 266, 268, 269, 272, 277, 279, 284, 288, 289, 293, 295, 297, 304, 308, 316, 319, 326, 328, 339]
d_Z 72 · witness weight 72 (claimed upper_bound)
witness found by @vprusso · single-block logical from the constituent cyclic code (exact, not sampled) · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 72 qubits)
[343, 354, 356, 363, 366, 374, 378, 385, 387, 389, 393, 394, 398, 403, 405, 410, 413, 414, 416, 418, 419, 422, 424, 429, 436, 446, 447, 449, 452, 455, 460, 480, 481, 486, 490, 491, 497, 507, 510, 511, 514, 517, 518, 519, 520, 529, 530, 533, 534, 544, 548, 550, 569, 572, 577, 579, 580, 581, 590, 591, 603, 610, 612, 623, 630, 641, 644, 651, 662, 663, 665, 672]
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 32 · H_Z 32
qubit degrees H_X 16 · H_Z 16
trapping sets H_X (1,16)×682 (2,24)×1364 (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
(1,16): 682 (2,24): 1364 (2,26): 8525 (2,28): 26598 (2,30): 84909
trapping sets H_Z (1,16)×682 (2,24)×1364 (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
(1,16): 682 (2,24): 1364 (2,26): 8525 (2,28): 26598 (2,30): 84909

Construction & provenance

authors @kessler-frost
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized bicycle on Z_341; A=[0, 1, 2, 4, 12, 33, 56, 84, 89, 97, 145, 176, 265, 270, 287, 310]; B=[0, 2, 44, 64, 84, 99, 121, 132, 168, 190, 231, 261, 275, 283, 301, 319].
model GPT-6 Astra (openai-codex/gpt-6-astra) (claimed, not verified)
builds on https://github.com/unitaryfoundation/qldpc-challenge/tree/8933cda94eb6beb803cbaad37d925f8d2a8fadcc
date 2026-09-06
notes Witness-backed upper bound; literature novelty unverified. {"engine": "upstream gf2_fast.dem_rand_witness", "pair_depth": 24, "proposal_id": "b6d86d076d1b5806", "rung": 4, "seconds": 211.35302416599006, "seed": 3952028553706826964, "side": "X", "source_sha256": "d2ad08dffbec95b4650dd30d68275f2db096994420cb377580cffcbb14bf3be1", "threads": 6, "trials": 2000000, "upstream_commit": "8933cda94eb6beb803cbaad37d925f8d2a8fadcc"} Distance corrected from d<=79 to d<=76 using the verified weight-76 X and Z witnesses reported in issue #942. The issue's verification checks place both witnesses in the appropriate opposite-check kernels and outside the stabilizer row spaces; the search budget is not reported.
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

[[682,172,72]]: distance revision of the board's [[682,172,76]] entry

Revision history

[[682,172,72]] supersedes the board's [[682,172,76]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance claim is corrected. For a generalized-bicycle pair with g = gcd(b, x^m - 1), every nonzero word u of the cyclic code whose nonzeros are the roots of g gives the single-block operator (u | 0), which commutes with every Z check and is not a stabilizer. A weight-72 word of that [341,96] constituent code, found by information-set search on the small code and re-validated against this entry's check matrices, together with its transport to the Z side, exhibits a weight-72 X-logical and a weight-72 Z-logical, so the previous witness-backed bound d <= 76 was overstated and the honest parameter set is [[682,172,72]]. The headline falls from kd^2/n = 1456.7 to 1307.4. Each lighter witness is carried in the entry with the budget it was found at and survived; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

The witnesses are not sampled on the full code: they are a weight-72 codeword of the [341,96] constituent cyclic code placed on one block, and its transport to the other side, each re-validated here (in the kernel of the opposite side's checks, outside the row space of its own side). The sampling-budget fields in witness_provenance therefore carry the placeholder 1 and the tool field names the construction. The constituent code bounds every generalized-bicycle pair with the same gcd the same way.

| side | claimed | lightest logical found | trials | seed | CPU-verified | |---|---|---|---|---|---| | X | 76 | 72 | 1 | 0 | yes | | Z | 76 | 72 | 1 | 0 | yes |

The sibling entry [[682,172,76]] with check weight 28 sits exactly at its own constituent cap of 76 and is unaffected. Score kd^2/n for this entry falls from 1456.7 to 1307.4.

Original note, with the file paths updated

[[682,172,79]] — cyclic generalized bicycle with witnessed distance upper bounds

Direction & hypothesis

Target: the unrestricted, weight-9plus cell, with at most 700 qubits and maximum check weight 32. The hypothesis was that sparse cyclic-polynomial pairs with a large shared divisor could improve the scalar score without exceeding those limits.

At upstream commit fb3430e7a7a09b083dca833e4ade5d6e06ef0441, the checked global leader was codes/682-182-76.json, with k*d^2/n = 1541.3958944281526. This submission has a claimed score of 1573.9765395894428, a 2.1137% increase. It does not dominate that entry componentwise: k decreases from 182 to 172 while the witnessed distance bound increases from 76 to 79.

The claim is d <= 79, not an exact distance certificate. Both CSS sides have explicit weight-79 nontrivial logicals in codes/682-172-72.json. No accepted entry at that checkpoint had both n=682 and k=172; exact-fingerprint and Weisfeiler-Lehman checks also found no match. This is a board-relative result, not a claim of new parameters in the literature or an exhaustive equivalence classification. Literature novelty remains unverified.

What was searched

The broader campaign explored cyclic generalized bicycles on cyclic groups of orders 331, 337, 339, 341, and 345. The order-341 bank contained 94 canonical proposal records. Classical sparse words were mined in polynomial ideals over GF(2), with masks excluding selected subideals and subgroup/norm constructions. Pairs were swept over relative multiplicative units modulo 341 and normalized under cyclic coordinate symmetries. Pair admission required shared-divisor degree at least 85 and combined support size at most 32; it was not distance validation.

For this pair, the two classical word records used seeds 3412026509717 and 341960005236450. Their individual ideal degrees were 96 and 86. The relative unit before canonicalization was 16; the shared divisor has degree 86. The exact canonical supports in Reproduction remove any need to replay that mining run.

Quantum screening used native gf2_fast.dem_rand_witness on the X side, with pair depth 24. Rung 0 used 8 threads, rung 1 used 10, and rungs 2 through 11 used 6. Seeds were computed with exact integer arithmetic:

seed = (2026090601 + int("b6d86d076d1b5806", 16) + 104729 * rung) % (2**63 - 1)

The circulant reversal/block-swap symmetry transports an X support to Z: q < 341 maps to 341 + (-q) % 341; otherwise it maps to (-(q-341)) % 341. Both transported witnesses were independently checked for commutation and nontriviality during packaging. This was not a second independent Z-side exploratory search. Every returned logical was retained; heavier later samples never replaced a lighter witness.

Evidence trail

The exploratory ladder below reports returned X weights separately from the best retained upper bound. Trial counts are cumulative X-side screening trials, not a lower-bound proof.

| Rung | Trials in rung | Cumulative trials | Returned weight | Best retained bound | |---|---:|---:|---:|---:| | 0 | 4,000 | 4,000 | 89 | 89 | | 1 | 200,000 | 204,000 | 83 | 83 | | 2 | 2,000,000 | 2,204,000 | 80 | 80 | | 3 | 2,000,000 | 4,204,000 | 81 | 80 | | 4 | 2,000,000 | 6,204,000 | 79 | 79 | | 5 | 2,000,000 | 8,204,000 | 81 | 79 | | 6 | 2,000,000 | 10,204,000 | 82 | 79 | | 7 | 2,000,000 | 12,204,000 | 79 | 79 | | 8 | 2,000,000 | 14,204,000 | 79 | 79 | | 9 | 2,000,000 | 16,204,000 | 80 | 79 | | 10 | 2,000,000 | 18,204,000 | 80 | 79 | | 11 | 2,000,000 | 20,204,000 | 81 | 79 |

The frozen submission SHA-256 is 39b95506a5c2bd093b41ca378edca35c2932f16a9c8e98c34503bdb7e0ded6ae. It includes the final model attribution; no JSON metadata changed between the following two uninterrupted acceptance runs.

Both ran unmodified verify/gate_changed.py from trusted upstream commit 5fea2b0042772be4024ffb07cf6781844f25434c against separate submitted trees. Both included a Python RIS target of 106,840 trials with a 240-second cap, the ldpc syndrome-decoder cross-check, and an 8,000,000-trial RIS-fast budget with four native threads. The Python trial target is not a claim that the time-capped search completed every requested trial.

| Independent gate seed | Outcome | Full isolated attempt wall time | |---|---|---:| | 1012401210 | Passed; no logical lighter than 79 found | 77.58 minutes | | 635370112 | Passed; no logical lighter than 79 found | 77.50 minutes |

The same frozen JSON also passed verify/validate_candidate.py against upstream commit f3efaf875e71bf1e6dad624d27160615387b3610. Relative to the deep-run base, the verifier implementation was unchanged; the acceptance workflow added a 90-minute job timeout. These local timings are not a hosted-runner performance guarantee. CI draws a fresh seed and may still refute the bound.

An earlier run with seed 377912191 was suspended during a user-requested pause. It later finished without a refutation, but it is excluded from acceptance evidence because suspension did not stop wall-clock budgets. Only the two uninterrupted runs above count.

Dead ends

A different order-345 pair initially supported a claimed [[690,182,77]] and survived an earlier deep run. A subsequent trusted gate with seed 359961143 found a weight-28 Z logical. That claim was retired rather than retried until a favorable seed appeared. The failed pair, using the same circulant convention as Reproduction but m=345, was:

A_bad = [0,1,3,18,33,47,63,70,193,216,253,254,273,276,285,288]
B_bad = [0,3,9,15,55,60,72,90,135,150,165,195,216,300,325,330]
Z_bad = [1,8,13,47,68,70,93,100,116,128,160,208,215,220,238,275,
         277,298,300,335,362,377,385,400,500,515,592,607]

Transporting that retained logical also lowered another order-345 pairing from an exploratory bound of 81 to 28. This motivated witness reuse across related pairs and the two-uninterrupted-gate acceptance rule. Sparse-pair eligibility, a high screening bound, and one passing random seed were not sufficient.

Tools

Coordinating model: GPT-6 Astra (openai-codex/gpt-6-astra), self-reported and matching provenance.model. Harness: Oh My Pi in Orca, with bounded generation and witness-transport workers. This attribution is not an independent attestation of every worker's served model.

The accepted pair used native classical mining, native quantum screening, NumPy-compatible matrix packaging, and the trusted Python/native/ldpc gates. Exploratory classical work was not acceptance evidence. This candidate's twelve native screening rungs used about 39.1 minutes of recorded wall time; the two uninterrupted isolated acceptance attempts used about 155.1 minutes combined. Those numbers exclude other candidates and interrupted work.

Reproduction

Let C(S) be the 341 by 341 binary circulant whose row i has ones at columns (i+s) % 341 for s in S. Use H_X = [C(A) | C(B)] and H_Z = [C(B).T | C(A).T]. Each check has weight 32, each column has weight 16 per CSS side, both check-matrix ranks are 255, and k=682-255-255=172.

From the repository root, this standard-library-only snippet reconstructs the exact sparse check rows and compares them with the submitted JSON:

import json
from pathlib import Path

m = 341
A = [0,1,2,4,12,33,56,84,89,97,145,176,265,270,287,310]
B = [0,2,44,64,84,99,121,132,168,190,231,261,275,283,301,319]
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/682-172-72.json").read_text())
assert doc["checks"]["X"] == hx
assert doc["checks"]["Z"] == hz
print("Exact check-matrix reconstruction matches the submission")

The submitted JSON contains the X and Z witnesses. Check it with:

uv run --frozen python verify/qldpc_verify.py codes/682-172-72.json

To replay the acceptance searches, use separate trusted-base and submitted checkouts as in the pinned acceptance workflow. Pin the t

Parity checks

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