[[674,170,76]] · QEC Challenge

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[[674,170,76]] d ≤

674

170

kd²/n

1456.855

X/Z

1.03

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Distance

X/Z asymmetry 1.03 · d_X ≤ 78, 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 78 · witness weight 78 (claimed upper_bound)

witness found by @DennisWayo · GB involution mirror of RIS-fast · found at 10⁶ trials · survived 10⁶ trials · 2026-09-30

witness operator (support, 78 qubits)

[6, 15, 18, 20, 22, 36, 50, 60, 62, 69, 73, 75, 76, 89, 91, 108, 120, 129, 130, 136, 138, 161, 166, 184, 201, 202, 210, 217, 223, 232, 238, 241, 264, 280, 282, 288, 305, 322, 334, 339, 342, 343, 349, 364, 372, 377, 381, 383, 407, 409, 413, 419, 424, 429, 462, 472, 483, 485, 494, 497, 513, 516, 525, 528, 529, 532, 533, 571, 590, 591, 592, 598, 611, 615, 645, 650, 652, 654]

d_Z 76 · witness weight 76 (claimed upper_bound)

witness found by @DennisWayo · verify/gate_changed.py RIS-fast · found at 4.7×10⁶ trials · survived 8×10⁶ trials · 2026-09-30

witness operator (support, 76 qubits)

[5, 7, 14, 21, 22, 23, 48, 53, 59, 69, 73, 75, 81, 90, 152, 158, 162, 174, 176, 187, 189, 215, 226, 228, 240, 243, 246, 291, 295, 303, 316, 323, 337, 338, 353, 363, 367, 380, 381, 390, 398, 401, 402, 411, 425, 427, 435, 436, 442, 474, 480, 482, 490, 502, 509, 513, 516, 522, 526, 532, 533, 534, 540, 550, 566, 567, 588, 589, 605, 621, 632, 644, 645, 649, 658, 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 32 · H_Z 32

qubit degrees H_X 16 · H_Z 16

trapping sets H_X (1,16)×674 (2,26)×3033 (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 (2,26): 3033 (2,28): 30330 (2,30): 97393

trapping sets H_Z (1,16)×674 (2,26)×3033 (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 (2,26): 3033 (2,28): 30330 (2,30): 97393

Construction & provenance

authors @DennisWayo

provenance submitted through the challenge

novelty novelty not audited

construction Frobenius-paired cyclic generalized-bicycle code over Z_337; a=[0, 1, 23, 26, 121, 130, 146, 148, 164, 168, 196, 205, 210, 247, 282, 308]; b=[0, 8, 29, 105, 157, 173, 184, 208, 220, 234, 291, 292, 294, 301, 332, 333]; b=a(x⁸) up to a cyclic shift; a is invariant under exponent multiplier 128; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].

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

date 2026-09-27

notes Corrected after the trusted verifier found a validated weight-76 Z logical at seed 7066436. The X-side weight-78 witness is retained, so the submitted bound is d<=76. The verifier signature collides with codes/674-170-76-b.json, but bounded trapping-set counts differ, indicating a distinct code rather than a duplicate.

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]] - Frobenius-paired generalized-bicycle code

Direction & hypothesis

The target was an unrestricted, weight-9plus generalized-bicycle (GB) cell near the existing Z_337 examples. The search hypothesis was that Frobenius-related support pairs could yield additional high-rate GB codes with comparatively large witnessed logical operators. This entry does not claim an exact distance or a new asymptotic family. It is a finite, witness-backed CSS code with d <= 76, k = 170, n = 674, and maximum check weight 32.

The code sits in the weight-9plus x unrestricted cell. Its kd^2/n score is 170*76^2/674 = 1456.854599. Admission is therefore not based on beating the headline score in another weight class, but on the challenge frontier rule in its own cell.

What was searched

The candidate came from a private cyclic GB campaign over Z_337. The miner searched sparse support pairs and then emphasized Frobenius-paired variants:

A = [0, 1, 23, 26, 121, 130, 146, 148, 164, 168, 196, 205, 210, 247, 282, 308]
B = [0, 8, 29, 105, 157, 173, 184, 208, 220, 234, 291, 292, 294, 301, 332, 333]

The relation used in the search was that B is generated from A by an exponent multiplier and cyclic shift, with A invariant under multiplier 128. The submitted CSS matrices are

H_X = [circ(A) | circ(B)]
H_Z = [circ(B)^T | circ(A)^T].

Both sides have 337 rows. The trusted verifier computes rank(H_X)=252, rank(H_Z)=252, and k=674-252-252=170.

Evidence trail

The original private package claimed d <= 78 from weight-78 X and Z witnesses. Before public submission it passed local structural screening and an 8M RIS-fast private screen on one seed. The public trusted verifier then found a lighter Z-type logical, so the submitted claim is corrected here to d <= 76.

The correcting witness was found by the trusted verifier in PR #2393:

seed = 7066436
method = verify/gate_changed.py RIS-fast
first reported at approximately 4,710,000 / 8,000,000 trials
side = Z
weight = 76

The witness is stored in codes/674-170-76-c.json as distance.Z.witness. The existing X witness of weight 78 is retained. Thus the earned distance bound is

distance.X = 78
distance.Z = 76
d = 76.

This is an upper-bound submission only. No lower bound, exact distance, or decoder-performance claim is made.

Duplicate and frontier status

The trusted verifier reports the same Weisfeiler-Leman signature as the existing board entry codes/674-170-76-b.json. This is not, by itself, a proof of code equivalence. In the PR discussion, @vprusso checked the corrected document and found that the fingerprints differ and bounded trapping-set counts differ while the WL signature, Tanner girth, and weight profile match. The trapping-set counts are permutation invariants, so the two entries should be treated as distinct codes sharing a WL signature rather than as a duplicate JSON representation of the same code.

The corrected candidate was also reported by that review to pass the challenge gate as a board-advancing, undominated entry in the weight-9plus x unrestricted cell, with advances_by empty. In other words, it joins the frontier at matching parameters rather than improving an existing axis.

Dead ends

The main dead end was the original d <= 78 claim. A private 8M RIS-fast run did not find a lighter logical, but the public trusted verifier did find the Z-side weight-76 witness with a different seed. This is why the PR is revised instead of rerun unchanged.

Nearby higher-claim candidates from the same general mining period also collapsed under structural or RIS-fast screening. The search workflow was therefore tightened after this PR to reject known verifier signatures and to require multiple independent fire passes before treating a package as ready.

Tools

The code was mined and packaged by @DennisWayo with OpenAI GPT-5 (Codex) assistance. Validation used the qLDPC Challenge verifier, the trusted verify/gate_changed.py refutation gate, and the repository's GF(2) accelerated RIS-fast path. The model field in the submitted JSON is OpenAI GPT-5 (Codex).

Reproduction

Work over F_2[x]/(x^337-1). Let A and B be the support lists above, and let circ(S) be the 337 by 337 binary circulant matrix whose first row has support S. Build

H_X = [circ(A) | circ(B)]
H_Z = [circ(B)^T | circ(A)^T].

The row spaces commute by the generalized-bicycle construction. Running the trusted verifier on codes/674-170-76-c.json checks CSS commutation, computes k=170, verifies the X and Z witnesses, and confirms the submitted d <= 76 bound.

Parity checks

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

H_X (337 checks, sparse supports)

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

H_Z (337 checks, sparse supports)

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