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[[682,172,78]] d ≤
n
682
k
172
d
78
kd²/n
1534.381
w
28
X/Z
1.17

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Distance

X/Z asymmetry 1.17 · d_X ≤ 78, d_Z ≤ 91 · w_X = 28, w_Z = 28 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 78 · witness weight 78 (claimed upper_bound)
witness operator (support, 78 qubits)
[14, 16, 23, 31, 36, 42, 48, 72, 77, 94, 96, 110, 115, 122, 123, 137, 142, 149, 152, 158, 160, 164, 174, 179, 183, 185, 193, 195, 228, 230, 239, 245, 260, 264, 272, 274, 276, 284, 287, 293, 305, 307, 339, 342, 370, 381, 393, 397, 399, 401, 434, 442, 446, 448, 450, 474, 483, 504, 505, 511, 514, 522, 524, 532, 554, 560, 589, 611, 626, 630, 631, 638, 644, 649, 651, 664, 672, 679]
d_Z 91 · witness weight 91 (claimed upper_bound)
witness operator (support, 91 qubits)
[11, 14, 17, 23, 38, 44, 47, 60, 65, 67, 70, 76, 85, 86, 87, 90, 91, 97, 102, 108, 109, 122, 133, 145, 157, 165, 167, 175, 189, 192, 194, 198, 207, 212, 213, 217, 223, 244, 254, 278, 286, 295, 309, 312, 317, 331, 357, 361, 364, 368, 370, 371, 383, 385, 388, 391, 411, 419, 421, 427, 449, 462, 466, 467, 468, 474, 480, 481, 491, 494, 495, 502, 508, 511, 517, 523, 548, 558, 565, 576, 579, 583, 589, 598, 603, 623, 649, 654, 656, 663, 669]
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 28 · H_Z 28
qubit degrees H_X 14 · H_Z 14
trapping sets H_X (1,14)×682 (2,22)×3751 (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
(1,14): 682 (2,22): 3751 (2,24): 18755 (2,26): 80135
trapping sets H_Z (1,14)×682 (2,22)×3751 (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
(1,14): 682 (2,22): 3751 (2,24): 18755 (2,26): 80135

Construction & provenance

authors @vaibhav-baj
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code over Z_341: H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T], with b a shifted Frobenius image x^s a(x4) of a (same zero set, shared divisor of degree 86, k=172); supports invariant under j -> 32 j (mod 341).
model Claude Claude Fable 5.1 (claimed, not verified)
date 2026-09-25
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

[[682,172,78]] — Frobenius-paired cyclic generalized bicycle on Z_341

Direction & hypothesis

Target: the unrestricted (weight ≤ 32) cell at the n ≤ 700 limit, in the same (n, k) row as the scalar leader codes/682-172-76.json (kd²/n = 1456.70, w = 28). notes/682-172-72.md states the constraint for this family: with shared divisor g, every word of the constituent [341, deg g] cyclic code is a single-block logical, so d ≤ d(C_g). The Gilbert–Varshamov bound for [341, 86] is 76, so the record sits at the GV limit of its constituent code and a higher d in this row needs a divisor whose [341, 86] code beats GV. The hypothesis was that such divisors exist among the sparse-generated ones if enough of them are sampled — and that the record's own structure tells how to sample them.

That structure: the record's supports are invariant under j → 32·j (mod 341), i.e. a(x³²) = a(x). With ord₃₄₁(2) = 10 this puts every Fourier value a(ζˢ) in GF(32) instead of GF(1024), so a degree-10 factor of x³⁴¹ − 1 divides a with probability 2⁻⁵ rather than 2⁻¹⁰; and b = x⁹⁷·a(x⁸) is a shifted Frobenius image of the same word, which shares its zero set and therefore the divisor. So the search is over single sparse symmetric words a, paired with a(x⁴).

What was searched

Sparse-first sampling of symmetric words: unions of f fixed points (multiples of 11) and (w − f)/2 orbits {j, 32j}, with (w, f) ∈ {(14,6), (14,4), (16,6), (16,8)}. Zero sets were read off by evaluating a at one representative of each of the 38 cyclotomic cosets in GF(1024) (~70k words/s). A word was kept when its zero set covered ≥ 86 degrees with ≥ 8 degree-10 cosets (rate ≈ 3·10⁻⁶).

Three seeds × ~90 min wall clock: ~25 million words sampled, 47 hits, 38 of them with the record's composition (x+1 · one quintic · eight decics, k = 172). Per hit: constituent cap by the verifier's own structural search (gf2_fast.circulant_gb_witness, 60k then 400k trials) on the pair (a, a(x⁴)); hits whose cap was below the d needed for their k were dropped. In the k = 172 row that was 37 of 38 (33 caps ≤ 16, two at exactly 76, one at 72 and 70); the one hit with cap 80 is this entry. Survivors entered an RIS-fast ladder of 1k → 20k → 500k → 3M trials per side (gf2_fast.distance_rand_witness), discarding as soon as the bound fell below the threshold.

Evidence trail

a = [17, 53, 89, 99, 112, 120, 174, 203, 209, 254, 285, 308, 330, 332]
b = [14, 15, 55, 68, 107, 117, 130, 139, 154, 209, 212, 297, 305, 334]   (= rotation of {4j mod 341 : j in a})

Shared divisor of degree 86, k = 172, both check weights 28 (w = 28).

| Stage | Budget | Lightest logical | |---|---:|---:| | structural cap (single-block words of C_g) | 60k trials | 80 | | structural cap | 400k trials | 80 | | RIS-fast | 1k / side | ≥ 80 | | RIS-fast | 20k / side | ≥ 80 | | RIS-fast | 500k / side | 78 | | RIS-fast | 3M / side | no lighter logical | | qldpc submit --dry-run (2k python RIS + 4M gf2_fast + verifier) | 4M / side | 78 (X), 91 (Z); verified, kd²/n = 1534.381 |

The claim is a witness-backed upper bound d ≤ 78, not an exact distance. Score at the bound: 172·78²/682 = 1534.4. Two k = 192 siblings from the same campaign (degree-96 divisors) also survived 3M trials, at d ≤ 74 (1541.6) and d ≤ 72 (1459.4); they are reported separately.

Dead ends

  • Random ideals of the record's factor pattern are barren: 12/12 sampled

    • degree-86 divisors had zero words of weight ≤ 16 generating the ideal (Stern ISD, 3k–10k RREF trials), while the record's own ideal has five (the Frobenius orbit a, a², a⁴, a⁸, a¹⁶). Every light word in random ideals was divisible by extra factors (k inflated to 182–242, caps 5–11): sub-ring words from 11·Z₃₄₁.

  • Symmetric words without fixed points are always degenerate: each orbit

    • {j, 32j} cancels mod 31, so a is divisible by x³¹ − 1; 25 such hits, all caps ≤ 11.

  • Frobenius partners are not interchangeable: on the record's own word,

    • (a, a²) and (a, a¹⁶) give d ≤ 15–17 at 2k trials; (a, a⁴) and (a, a⁸) give 86–87 at 20k. Only the latter were laddered.

  • 33 of 38 k = 172 hits had constituent caps ≤ 16: a sparse symmetric

    • generator does not by itself make the constituent code good.

  • Earlier sweeps of bivariate-bicycle and 2BGA families at high k (separate

    • fieldnote): 473 of 473 candidates passing an (n,k,d,w) screen were direct sums, caught only by the verifier's connectivity checks.

Tools

Coordinating model: Claude Fable 5.1 (Claude Code), matching provenance.model; human author @vaibhav-baj. Repo tooling: polynomial and circulant helpers from research/cyclic_gb.py, the C++ accelerator verify/gf2_fast.cpp built with MinGW-w64 (GCC 16.1), the verifier's structural and RIS-fast searches as the ladder. Compute: 3 × 4 threads for ~1.5 h of sampling and laddering, plus the dry runs, on one laptop. Distances are randomized upper bounds; the public verifier is the only judge.

Reproduction

Let C(S) be the 341 × 341 binary circulant whose row i has ones at columns (i + s) mod 341 for s ∈ S. With a and b above, H_X = [C(a) | C(b)] and H_Z = [C(b)ᵀ | C(a)ᵀ]. Equivalently b is any rotation of {4j mod 341 : j ∈ a}. Sampling seed 22 of the sparse-first miner described above.

Parity checks

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