[[674,170,76]] · QEC Challenge

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[[674,170,76]] d ≤

674

170

kd²/n

1456.855

X/Z

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Distance

X/Z asymmetry 1 · d_X ≤ 76, d_Z ≤ 76 · 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 76 · witness weight 76 (claimed upper_bound)

witness found by @vprusso · gf2_fast.distance_rand_witness pd8; verified mirror of Z · found at 6×10⁶ trials · 2026-09-24

witness operator (support, 76 qubits)

[1, 5, 13, 30, 45, 50, 60, 66, 87, 99, 123, 130, 134, 135, 153, 160, 161, 170, 185, 208, 213, 222, 238, 257, 265, 271, 280, 296, 309, 311, 318, 319, 326, 345, 346, 366, 375, 376, 381, 387, 388, 412, 413, 431, 440, 447, 455, 458, 464, 465, 480, 489, 492, 496, 500, 504, 514, 517, 523, 527, 535, 545, 550, 551, 553, 566, 567, 576, 586, 587, 628, 637, 649, 659, 667, 670]

d_Z 76 · witness weight 76 (claimed upper_bound)

witness found by @vprusso · gf2_fast.distance_rand_witness pd8 · found at 6×10⁶ trials · 2026-09-24

witness operator (support, 76 qubits)

[4, 7, 15, 25, 37, 46, 87, 88, 98, 107, 108, 121, 123, 124, 129, 139, 147, 151, 157, 160, 170, 174, 178, 182, 185, 194, 209, 210, 216, 219, 227, 234, 243, 261, 262, 286, 287, 293, 298, 299, 308, 328, 329, 348, 355, 356, 363, 365, 378, 394, 403, 409, 417, 436, 452, 461, 466, 489, 504, 513, 514, 521, 539, 540, 544, 551, 575, 587, 608, 614, 624, 629, 644, 661, 669, 673]

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)×674 (2,24)×337 (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): 674 (2,24): 337 (2,26): 4044 (2,28): 28308 (2,30): 97056

trapping sets H_Z (1,16)×674 (2,24)×337 (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): 674 (2,24): 337 (2,26): 4044 (2,28): 28308 (2,30): 97056

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction m337 cyclic GB; ideal=23331505384229193970289181; A=[24, 27, 81, 100, 131, 145, 149, 164, 177, 182, 183, 192, 204, 269, 277, 306]; B=[34, 54, 58, 63, 65, 94, 96, 97, 108, 142, 187, 213, 243, 259, 319, 324]; B=a(x⁴), HX=[C(a)|C(b)], HZ=[C(b)^T|C(a)^T]

builds on arXiv:2605.14173v1

date 2026-09-24

notes Known univariate-bicycle family; literature novelty unverified. The submitted distance is an upper bound from the lowest preserved original-matrix witnesses. Public audit evidence records exact search budgets, raw native supports, independently checked mirrors, and the finite permutation-inequivalence comparison.

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

[[674,170,76]] — degree-85 univariate bicycle, instance 067-f2

Direction & hypothesis

The target was the unrestricted headline score 1456.703812, from [[682,172,76]]. This is an instance of the known univariate-bicycle family with Frobenius exponent 2, b(x)=a(x^4), not a new family; see Rabeti–Mahdavifar, arXiv:2605.14173v1. The specific instance's novelty against the literature remains unverified.

The final claim is d <= 76, maximum check weight 32, score 170*76^2/674 = 1456.854599. This is 0.150787, or 0.01035%, above the posted score; the improvement is narrow and uses weight 32 checks versus the incumbent's weight 28. There is no exact-distance or hardware-performance claim.

What was searched

An initial constructor campaign searched 85 previously unvisited degree-84 cyclic-ideal representatives at 5,000 randomized RREF proposals each: 425,000 classical proposals, using NumPy seeds 924600000+catalog index. Six sparse words yielded 24 variants with b(x)=a(x^(2^s)), s in {1,2,3,7}; 12 survived the shallow score threshold. This instance is index 67, word 0, s=2. Its weight 16 word appeared at proposal 2489, seed 924600067. Its common gcd includes an additional x+1 factor, giving degree 85 and k=170. These constructor trials are not distance trials.

Evidence trail

Every value is a witnessed upper bound. Raw native supports, exact seeds, search parameters, and direct/mirror provenance are retained in the accompanying [public evidence](../research/evidence/vprusso-ub337-067-f2.json). Initial one-trial Python packaging documents were overwritten by the screen; later reproducibility replays are labeled separately, not counted as original receipts or native confirmation.

| Stage | Budget | Returned weight | | --- | --- | --- | | Coefficient-fixed j=1,3,7 | 2k X trials each; pair depth 32; one thread; seeds 924716703, 924716705, 924716709 | 84, 84, 84 | | Single-block structural screen | 20k per side and block; pair depth 16; two threads; seed 924706702 | 84 | | Full-matrix screen | 20k/side; pair depth 64; two threads; seed 924706702 | 83 | | Fresh general audit | 100k/side; pair depth 64; two threads; seed 924830003 | 82 | | Fresh general rung | 2,000,004 actual native trials/side (2M requested); pair depth 8; six threads; seed 924900067 | 78, directly on X | | Fresh continuation | 6M/side; pair depth 8; six threads; seed 924906067 | 76, directly on Z | | Default time-capped official gate | seed 924995067; 62.259 seconds | passed: true; no lighter logical returned; no exact or WL duplicate |

The mirror of every native winner was independently checked on the opposite Pauli side. A mirror is not an additional independent search. The native wrapper rounds each thread's share upward: the completed 2M request therefore executes 2,000,004 trials per side. The completed full-matrix general total is 8,120,004 trials per side, separately from structural and restricted searches. The final Z76 was returned by the six-million-trial continuation; X76 is its independently checked block-swap/reversal mirror. The two fresh rungs alone total 8,000,004 native trials per side. The time-capped gate's configured trial limit is not a completed-trial count.

The coefficient-fixed screens constrained each block by v[i]=v[(2^j*i) mod 337] while retaining the original check matrix and full original logical basis. They are physical-subspace searches, not automorphism or lower-bound claims.

Dead ends

Twelve of the initial 24 variants failed the shallow threshold. A separate k=168 candidate, 049-f3, fell 84→82 after 100k fresh general trials per side and then to 76 in an 8M request. Its score 1439.715134 did not beat the headline despite passing its default time-capped gate. That decline motivated the fresh continuation here; its audit budget and witnesses do not belong to this matrix pair.

The other k=170 finalist, 036-f2, fell from 80 to 78 and then to 71 in its independent 2M and 6M rungs. Its mixed Z71 support and checked X mirror are retained in the public evidence; they are not witnesses for this submitted matrix pair.

Twelve additional Frobenius variants of the two weight 16 constructors were later shown to be coordinate-permutation aliases of the previously screened s=1,2,3 cases. Their validated transported supports are preserved separately and counted as neither new code classes nor fresh original-matrix trials.

Tools

Contributor: @vprusso. NumPy and trusted bit-packed GF(2) RREF constructed the code. The repository's unchanged native structural, full-matrix, and DEM routines produced witnesses, checked on the original matrices and saved through the research kit. The final gate is verify/validate_candidate.py. No GPU was used. The 85-ideal constructor stage took about 128 seconds, the early general audit about 65 seconds, and the fresh 2M rung about 430 seconds. The six-million-trial continuation took 1401.906 seconds; the default official gate took 62.259 seconds.

Reproduction

Work over F_2[x]/(x^337+1), with

A = [24, 27, 81, 100, 131, 145, 149, 164, 177, 182, 183, 192, 204, 269, 277, 306]
B = [34, 54, 58, 63, 65, 94, 96, 97, 108, 142, 187, 213, 243, 259, 319, 324]

Set a(x)=sum(x^i for i in A); B is exactly 4*A modulo 337. Define C(a)[r,c]=a[(c-r) mod 337], then HX=[C(a)|C(b)] and HZ=[C(b)^T|C(a)^T]. Both sides have 337 rows, rank 252, row weight 32, and column weight 16. Circulant commutation gives CSS orthogonality and k=674-252-252=170. Integer bit i encodes the coefficient of x^i:

degree 84 generator = 23331505384229193970289181
degree 21 factors = [2332367, 2420557, 2720553, 2816251]
common gcd g = (x+1)*degree 84 generator = 65083167261774274452856359

The two block projections of each stabilizer row space have rank 252, so both are injective. The canonical projection-ideal generator over all 336 unit multipliers is 40596226193011322631504845; both compared k=170 board controls have 39019755261139131293320123, and the other finalist has 39055717386231510123236041. Their ideal orbits are disjoint. The injective-projection Sylow argument in the [accompanying fieldnote](../fieldnotes/2026-09-24-ub337-permutation-inequivalence.md) excludes arbitrary qubit-permutation equivalence, optionally with global H, between these exact compared matrices. This does not settle arbitrary local Clifford equivalence or literature-wide novelty.

Parity checks

X-checks 337 (max weight 32) · Z-checks 337 (max weight 32)

H_X (337 checks, sparse supports)

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

H_Z (337 checks, sparse supports)

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