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[[570,12,88]] d ≤
n
570
k
12
d
88
kd²/n
163.032
w
32
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 88, d_Z ≤ 88 · 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 88 · witness weight 88 (claimed upper_bound)
witness operator (support, 88 qubits)
[6, 11, 27, 40, 44, 52, 54, 66, 75, 81, 93, 102, 104, 105, 117, 121, 130, 131, 134, 141, 148, 151, 152, 158, 164, 169, 170, 173, 176, 178, 182, 191, 199, 203, 217, 220, 234, 249, 254, 267, 269, 280, 285, 290, 301, 312, 317, 320, 322, 323, 346, 362, 365, 374, 376, 393, 396, 397, 408, 409, 415, 417, 421, 424, 434, 438, 441, 444, 445, 449, 450, 452, 467, 468, 470, 472, 488, 491, 495, 498, 507, 535, 536, 538, 541, 545, 549, 556]
d_Z 88 · witness weight 88 (claimed upper_bound)
witness operator (support, 88 qubits)
[0, 14, 21, 25, 29, 32, 34, 35, 63, 72, 75, 79, 82, 98, 100, 102, 103, 118, 120, 121, 125, 126, 129, 132, 136, 146, 149, 153, 155, 161, 162, 173, 174, 177, 194, 196, 205, 208, 224, 247, 248, 250, 253, 258, 269, 280, 290, 301, 303, 316, 321, 336, 350, 353, 367, 371, 379, 388, 392, 394, 397, 400, 401, 406, 412, 418, 419, 422, 429, 436, 439, 440, 449, 453, 465, 466, 468, 477, 489, 495, 504, 516, 518, 526, 530, 543, 559, 564]
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 13–19 (mean 16.0) · H_Z 13–19 (mean 16.0)
trapping sets H_X (1,13)×285 (2,22)×3705 (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
(1,13): 285 (1,19): 285 (2,22): 3705 (2,24): 15105 (2,26): 5130 (2,28): 12540 (2,30): 29925 (2,32): 3705 (2,34): 8550 (2,36): 15960
trapping sets H_Z (1,13)×285 (2,22)×3705 (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
(1,13): 285 (1,19): 285 (2,22): 3705 (2,24): 15105 (2,26): 5130 (2,28): 12540 (2,30): 29925 (2,32): 3705 (2,34): 8550 (2,36): 15960

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Cyclic generalized-bicycle code on the ring x285 - 1 with a(x) = x15 + x38 + x44 + x47 + x98 + x105 + x116 + x158 + x194 + x214 + x216 + x241 + x250, b(x) = x63 + x101 + x105 + x106 + x108 + x121 + x125 + x158 + x191 + x198 + x204 + x230 + x240 + x241 + x257 + x260 + x277 + x282 + x283; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-09-24
notes Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed.
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

[[570,12,88]] weight-32 cyclic generalized-bicycle

Hypothesis

Cyclic generalized-bicycle codes at check weight 32 cover a wide blocklength range, and the board's coverage of that range is uneven: there are stretches of n where no entry sits near the (k, d) the family can reach. A broad randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work, finds the gaps.

Construction

ring x^285 - 1 a(x) = x^15 + x^38 + x^44 + x^47 + x^98 + x^105 + x^116 + x^158 + x^194 + x^214 + x^216 + x^241 + x^250 b(x) = x^63 + x^101 + x^105 + x^106 + x^108 + x^121 + x^125 + x^158 + x^191 + x^198 + x^204 + x^230 + x^240 + x^241 + x^257 + x^260 + x^277 + x^282 + x^283 H_X = [circ(a) | circ(b)] H_Z = [circ(b)^T | circ(a)^T]

n = 2m, and k = 2 deg gcd(a, b, x^m - 1), computed by Euclid before any matrix work so that most draws are discarded for free.

What was swept

One loop draws a ring size and a weight split, samples the two sparse polynomials, computes k by Euclid, and runs a cheap 60k-trial distance screen. A draw survives only if the resulting (n, k, d, w) is undominated on the live board snapshot. Surviving draws go through an escalating ladder of 400k, 2M and 8M random information-set trials, with the board comparison repeated at each rung so a candidate that collapses is dropped as soon as it stops being interesting.

The single-block check

General RIS over all 2m columns is close to blind to a logical supported entirely on one block. Such a vector u satisfies a(x) u(x) = 0 mod x^m - 1, which puts u in the ideal generated by h = (x^m - 1) / gcd(a, x^m - 1), so it can be searched directly in a space of dimension deg h rather than 2m. This matters: a previous submission of mine survived 150M general RIS trials at weight 74 and was then refuted by a weight-64 logical sitting entirely in one block, which the ideal search finds in seconds. Every candidate here is checked that way before the distance is believed, and any candidate whose single-block bound comes in below the ladder is dropped rather than submitted.

Distance ladder

Witness search runs on each side separately, so a run that happens to find one side cannot leave the other without a witness. Both witnesses are re-checked directly against H: in the kernel of the opposite matrix, and outside the row space of its own.

What it advances

Score kd^2/n = 163.032 at check weight 32. Undominated in its cell against the board at submission time.

Boundary

The distance is an upper bound from witness search, not a proof. Literature novelty is unverified: cyclic GB codes are a classical family and these parameters may appear in the 2BGA literature.

Parity checks

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