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[[384,12,17]] d ≤
n
384
k
12
d
17
kd²/n
9.031
w
8
g
0.0045
r
6.7082
layers
2

Share this result

Distance

d_X 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[3, 7, 27, 28, 51, 75, 97, 100, 121, 123, 124, 145, 255, 257, 279, 280, 345, 346]
d_Z 17 · witness weight 17 (claimed upper_bound)
witness operator (support, 17 qubits)
[7, 8, 10, 24, 47, 63, 112, 188, 191, 192, 194, 195, 208, 211, 212, 218, 247]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 6.708
X checkZ checkqubit site (228)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary planar bivariate-bicycle code (Liang-Eberhardt-Chen, arXiv:2504.08887) on a 10x23 bilayer grid: support f=[(0,0),(1,0),(2,3),(2,-2)], g=[(0,0),(0,1),(-1,-1),(-1,3)] (w8 flagship family from research/local2d/boundary_engine.py; directional anyon condensation, X boundary terms on top/bottom, Z on left/right).
model DeepSeek V4 Flash 0731 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-08-09
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (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

[[384,12,17]] — open-boundary planar BB code, bilayer weight-8

Direction & hypothesis

Target cell: weight-8 x local-2d-bilayer, operational efficiency K = kd^2/n. This is the "populate the sparse 2D-local cells" route (research/candidates/_planar_pop_sweep.py): open-boundary planar bivariate-bicycle codes (Liang--Eberhardt--Chen, arXiv:2504.08887) are genuinely 2D-local by construction (qubits on a bilayer grid, every check within a bounded radius), so every staged code enters a local-2d-* cell rather than the unrestricted cell. The sparse cells — notably weight-8 x local-2d-bilayer — had few entries, and the mechanism's flagship [[288,8,12]] already validated against the paper's Table V.

This entry, [[384,12,17]], is the best of the open-boundary sweep's results: K = 12·17²/384 = 9.03, beating the cell's previous leader [[263,16,12]] (K = 8.76) and [[216,15,11]] (K = 8.40).

What was searched

_planar_pop_sweep.py sweeps the (S_f, S_g) support pairs of the w6/w8 planar-BB families over lattice sizes (Lx, Ly) with 2·Lx·Ly <= 700, builds each via boundary_engine.build_planar (directional anyon condensation, greedy corner-drop for anticommutation), requires CSS + k stable, screens distance_rand at 300 trials, dedups by fingerprint, and stages every distinct valid code under research/candidates/planar_pop/. 409 hits total; the top by eff is this 384-qubit family member computed at Lx=10, Ly=23.

Evidence trail

  • Construction: planar BB, supports f=[(0,0),(1,0),(2,3),(2,-2)],

    • g=[(0,0),(0,1),(-1,-1),(-1,3)], 10x23 bilayer grid; n = 384, k = 12.

  • Check weights: max weight 8 (X: 237 rows incl. w8 bulk + w3/4/6/7

    • boundary rows; Z: 222 rows incl. w8 bulk + w2-7 boundary terms) — the verifier computes weight-8.

  • Locality: 2 layers, interaction radius r = 6.7082 = 3*sqrt(5) (within the

    • local-2d-bilayer cap of 7.0), computed by the verifier from the layout.

  • Distance: witness-backed upper bound, d <= 17 (X/Z witnesses in the file).

    • Deep refutation pass CLEAR: 3 independent RIS seeds at 71,080 trials each (240s budget) + the syndrome-decoder cross-check — no lighter logical found. This is the same depth CI applies to a record claim (it is what refuted the earlier [[432,8,58]] draft at weight 24).

  • Gate: verify/validate_candidate.py -> passed: true,

    • board_advancing: true, dominated_by: [] in weight-8 x local-2d-bilayer.

Dead ends

  • The sweep's 254 w9+ x unrestricted(r=7.1) and 14 w9+ x bilayer staged

    • codes never reach a board cell (r > 7.0 or uncontrolled w) — they are drafts only.

  • No weight-8 x local-2d-single or weight-4 x local-2d-single candidate

    • exists yet: every open-boundary planar-BB code is a bilayer by construction (2 qubits per site), so the single-layer sparse cells stay empty for this route.

  • The older staged [[474,12,21]] (eff 11.2 in the sweep log) is not yet

    • staged/regated as a file; if it materializes it would be an even stronger entry — this submission is the strongest *gated* result so far.

Tools

Model: DeepSeek V4 Flash 0731 (matches provenance.model). Repo kit (research/local2d/boundary_engine.py, research/local2d/planar.py, research/kit/submit.py), verify/validate_candidate.py as the gate, verify/gate_changed.py --with ldpc for the deep refutation. Compute: the deep pass was the dominant cost (~12 min over 3 seeds + decoder).

Reproduction

import sys; sys.path += ["research/local2d", "research/kit", "verify"]
from boundary_engine import build_planar
from planar import grid_coordinates
HX, HZ, info = build_planar(10, 23, [(0,0),(1,0),(2,3),(2,-2)],
                            [(0,0),(0,1),(-1,-1),(-1,3)], cleanup=True)
# n=384, k=12, w=8; RIS d <= 17; deep-refutation CLEAR

Source file: research/candidates/planar_pop/384-12-17-clean.json.

Parity checks

X-checks 237 · Z-checks 222
H_X (237 checks, sparse supports)
[2, 23, 28, 184, 188, 207, 208] [3, 24, 29, 185, 189, 208, 209] [4, 25, 30, 186, 190, 209, 210] [5, 26, 31, 187, 191, 210, 211] [6, 27, 32, 188, 192, 211, 212] [7, 28, 33, 189, 193, 212, 213] [8, 29, 34, 190, 194, 213, 214] [9, 30, 35, 191, 195, 214, 215] [10, 31, 36, 192, 196, 215, 216] [11, 32, 37, 193, 197, 216, 217] [12, 33, 38, 194, 198, 217, 218] [13, 34, 39, 195, 199, 218, 219] [14, 35, 40, 196, 200, 219, 220] [15, 36, 41, 197, 201, 220, 221] [16, 37, 42, 198, 202, 221, 222] [17, 38, 43, 199, 203, 222, 223] [18, 39, 44, 200, 204, 223, 224] [19, 40, 45, 201, 205, 224, 225] [2, 25, 46, 51, 206, 210, 229, 230] [3, 26, 47, 52, 207, 211, 230, 231] [4, 27, 48, 53, 208, 212, 231, 232] [5, 28, 49, 54, 209, 213, 232, 233] [6, 29, 50, 55, 210, 214, 233, 234] [7, 30, 51, 56, 211, 215, 234, 235] [8, 31, 52, 57, 212, 216, 235, 236] [9, 32, 53, 58, 213, 217, 236, 237] [10, 33, 54, 59, 214, 218, 237, 238] [11, 34, 55, 60, 215, 219, 238, 239] [12, 35, 56, 61, 216, 220, 239, 240] [13, 36, 57, 62, 217, 221, 240, 241] [14, 37, 58, 63, 218, 222, 241, 242] [15, 38, 59, 64, 219, 223, 242, 243] [16, 39, 60, 65, 220, 224, 243, 244] [17, 40, 61, 66, 221, 225, 244, 245] [18, 41, 62, 67, 222, 226, 245, 246] [19, 42, 63, 68, 223, 227, 246, 247] [25, 48, 69, 74, 228, 232, 251, 252] [26, 49, 70, 75, 229, 233, 252, 253] [27, 50, 71, 76, 230, 234, 253, 254] [28, 51, 72, 77, 231, 235, 254, 255] [29, 52, 73, 78, 232, 236, 255, 256] [30, 53, 74, 79, 233, 237, 256, 257] [31, 54, 75, 80, 234, 238, 257, 258] [32, 55, 76, 81, 235, 239, 258, 259] [33, 56, 77, 82, 236, 240, 259, 260] [34, 57, 78, 83, 237, 241, 260, 261] [35, 58, 79, 84, 238, 242, 261, 262] [36, 59, 80, 85, 239, 243, 262, 263] [37, 60, 81, 86, 240, 244, 263, 264] [38, 61, 82, 87, 241, 245, 264, 265] [39, 62, 83, 88, 242, 246, 265, 266] [40, 63, 84, 89, 243, 247, 266, 267] [41, 64, 85, 90, 244, 248, 267, 268] [42, 65, 86, 91, 245, 249, 268, 269] [48, 71, 92, 97, 250, 254, 273, 274] [49, 72, 93, 98, 251, 255, 274, 275] [50, 73, 94, 99, 252, 256, 275, 276] [51, 74, 95, 100, 253, 257, 276, 277] [52, 75, 96, 101, 254, 258, 277, 278] [53, 76, 97, 102, 255, 259, 278, 279] [54, 77, 98, 103, 256, 260, 279, 280] [55, 78, 99, 104, 257, 261, 280, 281] [56, 79, 100, 105, 258, 262, 281, 282] [57, 80, 101, 106, 259, 263, 282, 283] [58, 81, 102, 107, 260, 264, 283, 284] [59, 82, 103, 108, 261, 265, 284, 285] [60, 83, 104, 109, 262, 266, 285, 286] [61, 84, 105, 110, 263, 267, 286, 287] [62, 85, 106, 111, 264, 268, 287, 288] [63, 86, 107, 112, 265, 269, 288, 289] [64, 87, 108, 113, 266, 270, 289, 290] [65, 88, 109, 114, 267, 271, 290, 291] [71, 94, 115, 120, 272, 276, 295, 296] [72, 95, 116, 121, 273, 277, 296, 297] [73, 96, 117, 122, 274, 278, 297, 298] [74, 97, 118, 123, 275, 279, 298, 299] [75, 98, 119, 124, 276, 280, 299, 300] [76, 99, 120, 125, 277, 281, 300, 301] [77, 100, 121, 126, 278, 282, 301, 302] [78, 101, 122, 127, 279, 283, 302, 303] [79, 102, 123, 128, 280, 284, 303, 304] [80, 103, 124, 129, 281, 285, 304, 305] [81, 104, 125, 130, 282, 286, 305, 306] [82, 105, 126, 131, 283, 287, 306, 307] [83, 106, 127, 132, 284, 288, 307, 308] [84, 107, 128, 133, 285, 289, 308, 309] [85, 108, 129, 134, 286, 290, 309, 310] [86, 109, 130, 135, 287, 291, 310, 311] [87, 110, 131, 136, 288, 292, 311, 312] [88, 111, 132, 137, 289, 293, 312, 313] [94, 117, 138, 143, 294, 298, 317, 318] [95, 118, 139, 144, 295, 299, 318, 319] [96, 119, 140, 145, 296, 300, 319, 320] [97, 120, 141, 146, 297, 301, 320, 321] [98, 121, 142, 147, 298, 302, 321, 322] [99, 122, 143, 148, 299, 303, 322, 323] [100, 123, 144, 149, 300, 304, 323, 324] [101, 124, 145, 150, 301, 305, 324, 325] [102, 125, 146, 151, 302, 306, 325, 326] [103, 126, 147, 152, 303, 307, 326, 327] [104, 127, 148, 153, 304, 308, 327, 328] [105, 128, 149, 154, 305, 309, 328, 329] [106, 129, 150, 155, 306, 310, 329, 330] [107, 130, 151, 156, 307, 311, 330, 331] [108, 131, 152, 157, 308, 312, 331, 332] [109, 132, 153, 158, 309, 313, 332, 333] [110, 133, 154, 159, 310, 314, 333, 334] [111, 134, 155, 160, 311, 315, 334, 335] [117, 140, 161, 166, 316, 320, 340, 341] [118, 141, 162, 167, 317, 321, 341, 342] [119, 142, 163, 168, 318, 322, 342, 343] [120, 143, 164, 169, 319, 323, 343, 344] [121, 144, 165, 170, 320, 324, 344, 345] [122, 145, 166, 171, 321, 325, 345, 346] [123, 146, 167, 172, 322, 326, 346, 347] [124, 147, 168, 173, 323, 327, 347, 348] [125, 148, 169, 174, 324, 328, 348, 349] [126, 149, 170, 175, 325, 329, 349, 350] [127, 150, 171, 176, 326, 330, 350, 351] [128, 151, 172, 177, 327, 331, 351, 352] [129, 152, 173, 178, 328, 332, 352, 353] [130, 153, 174, 179, 329, 333, 353, 354] [131, 154, 175, 180, 330, 334, 354, 355] [132, 155, 176, 181, 331, 335, 355, 356] [133, 156, 177, 182, 332, 336, 356, 357] [134, 157, 178, 183, 333, 337, 357, 358] [0, 1, 2, 3, 4, 185] [1, 2, 3, 4, 5, 186] [2, 3, 4, 5, 6, 187] [3, 4, 5, 6, 7, 188] [4, 5, 6, 7, 8, 189] [5, 6, 7, 8, 9, 190] [6, 7, 8, 9, 10, 191] [7, 8, 9, 10, 11, 192] [8, 9, 10, 11, 12, 193] [9, 10, 11, 12, 13, 194] [10, 11, 12, 13, 14, 195] [11, 12, 13, 14, 15, 196] [12, 13, 14, 15, 16, 197] [13, 14, 15, 16, 17, 198] [14, 15, 16, 17, 18, 199] [15, 16, 17, 18, 19, 200] [16, 17, 18, 19, 20, 201] [17, 18, 19, 20, 21, 202] [18, 19, 20, 21, 22, 203] [2, 23, 28, 184, 188, 207, 208] [3, 24, 29, 185, 189, 208, 209] [4, 25, 30, 186, 190, 209, 210] [5, 26, 31, 187, 191, 210, 211] [6, 27, 32, 188, 192, 211, 212] [7, 28, 33, 189, 193, 212, 213] [8, 29, 34, 190, 194, 213, 214] [9, 30, 35, 191, 195, 214, 215] [10, 31, 36, 192, 196, 215, 216] [11, 32, 37, 193, 197, 216, 217] [12, 33, 38, 194, 198, 217, 218] [13, 34, 39, 195, 199, 218, 219] [14, 35, 40, 196, 200, 219, 220] [15, 36, 41, 197, 201, 220, 221] [16, 37, 42, 198, 202, 221, 222] [17, 38, 43, 199, 203, 222, 223] [18, 39, 44, 200, 204, 223, 224] [19, 40, 45, 201, 205, 224, 225] [0, 5, 185, 186] [1, 6, 186, 187] [2, 7, 187, 188] [3, 8, 188, 189] [4, 9, 189, 190] [5, 10, 190, 191] [6, 11, 191, 192] [7, 12, 192, 193] [8, 13, 193, 194] [9, 14, 194, 195] [10, 15, 195, 196] [11, 16, 196, 197] [12, 17, 197, 198] [13, 18, 198, 199] [14, 19, 199, 200] [15, 20, 200, 201] [16, 21, 201, 202] [17, 22, 202, 203] [163, 362, 366] [164, 363, 367] [165, 364, 368] [166, 365, 369] [167, 366, 370] [168, 367, 371] [169, 368, 372] [170, 369, 373] [171, 370, 374] [172, 371, 375] [173, 372, 376] [174, 373, 377] [175, 374, 378] [176, 375, 379] [177, 376, 380] [178, 377, 381] [179, 378, 382] [180, 379, 383] [140, 163, 339, 343, 363, 364] [141, 164, 340, 344, 364, 365] [142, 165, 341, 345, 365, 366] [143, 166, 342, 346, 366, 367] [144, 167, 343, 347, 367, 368] [145, 168, 344, 348, 368, 369] [146, 169, 345, 349, 369, 370] [147, 170, 346, 350, 370, 371] [148, 171, 347, 351, 371, 372] [149, 172, 348, 352, 372, 373] [150, 173, 349, 353, 373, 374] [151, 174, 350, 354, 374, 375] [152, 175, 351, 355, 375, 376] [153, 176, 352, 356, 376, 377] [154, 177, 353, 357, 377, 378] [155, 178, 354, 358, 378, 379] [156, 179, 355, 359, 379, 380] [157, 180, 356, 360, 380, 381] [163, 362, 366] [164, 363, 367] [165, 364, 368] [166, 365, 369] [167, 366, 370] [168, 367, 371] [169, 368, 372] [170, 369, 373] [171, 370, 374] [172, 371, 375] [173, 372, 376] [174, 373, 377] [175, 374, 378] [176, 375, 379] [177, 376, 380] [178, 377, 381] [179, 378, 382] [180, 379, 383] [139, 162, 338, 342, 362, 363] [162, 361, 365]
H_Z (222 checks, sparse supports)
[2, 3, 23, 27, 188, 208, 230] [3, 4, 24, 28, 184, 189, 209, 231] [4, 5, 25, 29, 185, 190, 210, 232] [5, 6, 26, 30, 186, 191, 211, 233] [6, 7, 27, 31, 187, 192, 212, 234] [7, 8, 28, 32, 188, 193, 213, 235] [8, 9, 29, 33, 189, 194, 214, 236] [9, 10, 30, 34, 190, 195, 215, 237] [10, 11, 31, 35, 191, 196, 216, 238] [11, 12, 32, 36, 192, 197, 217, 239] [12, 13, 33, 37, 193, 198, 218, 240] [13, 14, 34, 38, 194, 199, 219, 241] [14, 15, 35, 39, 195, 200, 220, 242] [15, 16, 36, 40, 196, 201, 221, 243] [16, 17, 37, 41, 197, 202, 222, 244] [17, 18, 38, 42, 198, 203, 223, 245] [18, 19, 39, 43, 199, 204, 224, 246] [19, 20, 40, 44, 200, 205, 225, 247] [25, 26, 46, 50, 210, 230, 252] [26, 27, 47, 51, 206, 211, 231, 253] [27, 28, 48, 52, 207, 212, 232, 254] [28, 29, 49, 53, 208, 213, 233, 255] [29, 30, 50, 54, 209, 214, 234, 256] [30, 31, 51, 55, 210, 215, 235, 257] [31, 32, 52, 56, 211, 216, 236, 258] [32, 33, 53, 57, 212, 217, 237, 259] [33, 34, 54, 58, 213, 218, 238, 260] [34, 35, 55, 59, 214, 219, 239, 261] [35, 36, 56, 60, 215, 220, 240, 262] [36, 37, 57, 61, 216, 221, 241, 263] [37, 38, 58, 62, 217, 222, 242, 264] [38, 39, 59, 63, 218, 223, 243, 265] [39, 40, 60, 64, 219, 224, 244, 266] [40, 41, 61, 65, 220, 225, 245, 267] [41, 42, 62, 66, 221, 226, 246, 268] [42, 43, 63, 67, 222, 227, 247, 269] [48, 49, 69, 73, 232, 252, 274] [49, 50, 70, 74, 228, 233, 253, 275] [50, 51, 71, 75, 229, 234, 254, 276] [51, 52, 72, 76, 230, 235, 255, 277] [52, 53, 73, 77, 231, 236, 256, 278] [53, 54, 74, 78, 232, 237, 257, 279] [54, 55, 75, 79, 233, 238, 258, 280] [55, 56, 76, 80, 234, 239, 259, 281] [56, 57, 77, 81, 235, 240, 260, 282] [57, 58, 78, 82, 236, 241, 261, 283] [58, 59, 79, 83, 237, 242, 262, 284] [59, 60, 80, 84, 238, 243, 263, 285] [60, 61, 81, 85, 239, 244, 264, 286] [61, 62, 82, 86, 240, 245, 265, 287] [62, 63, 83, 87, 241, 246, 266, 288] [63, 64, 84, 88, 242, 247, 267, 289] [64, 65, 85, 89, 243, 248, 268, 290] [65, 66, 86, 90, 244, 249, 269, 291] [71, 72, 92, 96, 254, 274, 296] [72, 73, 93, 97, 250, 255, 275, 297] [73, 74, 94, 98, 251, 256, 276, 298] [74, 75, 95, 99, 252, 257, 277, 299] [75, 76, 96, 100, 253, 258, 278, 300] [76, 77, 97, 101, 254, 259, 279, 301] [77, 78, 98, 102, 255, 260, 280, 302] [78, 79, 99, 103, 256, 261, 281, 303] [79, 80, 100, 104, 257, 262, 282, 304] [80, 81, 101, 105, 258, 263, 283, 305] [81, 82, 102, 106, 259, 264, 284, 306] [82, 83, 103, 107, 260, 265, 285, 307] [83, 84, 104, 108, 261, 266, 286, 308] [84, 85, 105, 109, 262, 267, 287, 309] [85, 86, 106, 110, 263, 268, 288, 310] [86, 87, 107, 111, 264, 269, 289, 311] [87, 88, 108, 112, 265, 270, 290, 312] [88, 89, 109, 113, 266, 271, 291, 313] [94, 95, 115, 119, 276, 296, 318] [95, 96, 116, 120, 272, 277, 297, 319] [96, 97, 117, 121, 273, 278, 298, 320] [97, 98, 118, 122, 274, 279, 299, 321] [98, 99, 119, 123, 275, 280, 300, 322] [99, 100, 120, 124, 276, 281, 301, 323] [100, 101, 121, 125, 277, 282, 302, 324] [101, 102, 122, 126, 278, 283, 303, 325] [102, 103, 123, 127, 279, 284, 304, 326] [103, 104, 124, 128, 280, 285, 305, 327] [104, 105, 125, 129, 281, 286, 306, 328] [105, 106, 126, 130, 282, 287, 307, 329] [106, 107, 127, 131, 283, 288, 308, 330] [107, 108, 128, 132, 284, 289, 309, 331] [108, 109, 129, 133, 285, 290, 310, 332] [109, 110, 130, 134, 286, 291, 311, 333] [110, 111, 131, 135, 287, 292, 312, 334] [111, 112, 132, 136, 288, 293, 313, 335] [117, 118, 138, 142, 298, 318, 341] [118, 119, 139, 143, 294, 299, 319, 342] [119, 120, 140, 144, 295, 300, 320, 343] [120, 121, 141, 145, 296, 301, 321, 344] [121, 122, 142, 146, 297, 302, 322, 345] [122, 123, 143, 147, 298, 303, 323, 346] [123, 124, 144, 148, 299, 304, 324, 347] [124, 125, 145, 149, 300, 305, 325, 348] [125, 126, 146, 150, 301, 306, 326, 349] [126, 127, 147, 151, 302, 307, 327, 350] [127, 128, 148, 152, 303, 308, 328, 351] [128, 129, 149, 153, 304, 309, 329, 352] [129, 130, 150, 154, 305, 310, 330, 353] [130, 131, 151, 155, 306, 311, 331, 354] [131, 132, 152, 156, 307, 312, 332, 355] [132, 133, 153, 157, 308, 313, 333, 356] [133, 134, 154, 158, 309, 314, 334, 357] [134, 135, 155, 159, 310, 315, 335, 358] [140, 141, 161, 165, 320, 341, 364] [141, 142, 162, 166, 316, 321, 342, 365] [142, 143, 163, 167, 317, 322, 343, 366] [143, 144, 164, 168, 318, 323, 344, 367] [144, 145, 165, 169, 319, 324, 345, 368] [145, 146, 166, 170, 320, 325, 346, 369] [146, 147, 167, 171, 321, 326, 347, 370] [147, 148, 168, 172, 322, 327, 348, 371] [148, 149, 169, 173, 323, 328, 349, 372] [149, 150, 170, 174, 324, 329, 350, 373] [150, 151, 171, 175, 325, 330, 351, 374] [151, 152, 172, 176, 326, 331, 352, 375] [152, 153, 173, 177, 327, 332, 353, 376] [153, 154, 174, 178, 328, 333, 354, 377] [154, 155, 175, 179, 329, 334, 355, 378] [155, 156, 176, 180, 330, 335, 356, 379] [156, 157, 177, 181, 331, 336, 357, 380] [157, 158, 178, 182, 332, 337, 358, 381] [23, 184] [46, 206] [69, 228] [92, 250] [115, 272] [138, 294] [161, 316] [0, 24, 185] [23, 47, 207] [46, 70, 229] [69, 93, 251] [92, 116, 273] [0, 1, 25, 186, 206, 228] [23, 24, 48, 208, 228, 250] [46, 47, 71, 230, 250, 272] [69, 70, 94, 252, 272, 294] [92, 93, 117, 274, 294, 316] [115, 116, 140, 296, 316, 339] [138, 139, 163, 318, 339, 362] [1, 2, 26, 187, 207, 229] [24, 25, 49, 209, 229, 251] [47, 48, 72, 231, 251, 273] [70, 71, 95, 253, 273, 295] [93, 94, 118, 275, 295, 317] [116, 117, 141, 297, 317, 340] [139, 140, 164, 319, 340, 363] [2, 3, 23, 27, 188, 208, 230] [25, 26, 46, 50, 210, 230, 252] [48, 49, 69, 73, 232, 252, 274] [71, 72, 92, 96, 254, 274, 296] [94, 95, 115, 119, 276, 296, 318] [117, 118, 138, 142, 298, 318, 341] [140, 141, 161, 165, 320, 341, 364] [3, 4, 23, 24, 28, 189, 209, 231] [26, 27, 46, 47, 51, 211, 231, 253] [49, 50, 69, 70, 74, 233, 253, 275] [72, 73, 92, 93, 97, 255, 275, 297] [95, 96, 115, 116, 120, 277, 297, 319] [118, 119, 138, 139, 143, 299, 319, 342] [141, 142, 161, 162, 166, 321, 342, 365] [0, 24, 185] [23, 47, 207] [46, 70, 229] [69, 93, 251] [92, 116, 273] [115, 139, 295, 338] [138, 162, 317, 338, 361] 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raw submission JSON