# Question 26067: A Cover Can Resist Every Single Deletion yet Be Larger than Another Cover

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0051-26067 · q-20261015-advance-20261115-r06-minimum-vertex-cover-0067



## Original question and givens

Use complete unique vertices=[c0, l0_0, l0_1, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7] and loop-free duplicate-free undirected edges=[[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]], candidate cover=[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7]. An edge needs at least one selected endpoint. Preserve source canonical subset order. Give (candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate).


- G001 — Use complete unique vertices=[c0, l0_0, l0_1, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7] and loop-free duplicate-free undirected edges=[[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]], candidate cover=[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7]. An edge needs at least one selected endpoint. Preserve source canonical subset order. Give (candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate).





## Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.


- [mko-minimum-vertex-cover](https://ocme.evemisslab.com/en/mko/mko-minimum-vertex-cover/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [mincover-minimal-not-minimum]

After

derived = [[candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate]]

Conditions: none

List the full source field order without JavaScript.Original modes select contract6/4/6/6 and IVT8/7/8 roles,without padding or answer-shape inference.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [[c0, l0_0, l0_1, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7]]

After

derived = [[c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7]]

Conditions: none

The carrier is nonempty with at most12 vertices;sort endpoints by UTF16 then edge families in English.Reject loops/reversed duplicates.An omitted candidate stays null,not an invented empty candidate.

Step identifiers and dependenciesRule: Mincover_complete_simple_graph_UTF16_English_and_optional_candidate · Uses: G001, S001





S003 · impliesBefore

source roles = [[c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]], 4096]

After

derived = [[3, 7, 11, 14, 15, 19, 23, 27, 30, 31, 35, 39, 43, 46, 47, 51, 55, 59, 62, 63, 67, 71, 75, 78, 79, 83, 87, 91, 94, 95, 99, 103, 107, 110, 111, 115, 119, 123, 126, 127, 131, 135, 139, 142, 143, 147, 151, 155, 158, 159, 163, 167, 171, 174, 175, 179, 183, 187, 190, 191, 195, 199, 203, 206, 207, 211, 215, 219, 222, 223, 227, 231, 235, 238, 239, 243, 247, 251, 254, 255, 259, 263, 267, 270, 271, 275, 279, 283, 286, 287, 291, 295, 299, 302, 303, 307, 311, 315, 318, 319, 323, 327, 331, 334, 335, 339, 343, 347, 350, 351, 355, 359, 363, 366, 367, 371, 375, 379, 382, 383, 387, 391, 395, 398, 399, 403, 407, 411, 414, 415, 419, 423, 427, 430, 431, 435, 439, 443, 446, 447, 451, 455, 459, 462, 463, 467, 471, 475, 478, 479, 483, 487, 491, 494, 495, 499, 503, 507, 510, 511, 515, 519, 523, 526, 527, 531, 535, 539, 542, 543, 547, 551, 555, 558, 559, 563, 567, 571, 574, 575, 579, 583, 587, 590, 591, 595, 599, 603, 606, 607, 611, 615, 619, 622, 623, 627, 631, 635, 638, 639, 643, 647, 651, 654, 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l0_1, l1_0, l1_1, l1_4, l1_5], [c0, c1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_5], [c0, c1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5], [c0, c1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], [c0, c1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5], [c0, c1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], [c0, c1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [c0, c1, l1_6], [c0, c1, l0_0, l1_6], [c0, c1, l0_1, l1_6], [c1, l0_0, l0_1, l1_6], [c0, c1, l0_0, l0_1, l1_6], [c0, c1, l1_0, l1_6], [c0, c1, l0_0, l1_0, l1_6], [c0, c1, l0_1, l1_0, l1_6], [c1, l0_0, l0_1, l1_0, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_6], [c0, c1, l1_1, l1_6], [c0, c1, l0_0, l1_1, l1_6], [c0, c1, l0_1, l1_1, l1_6], [c1, l0_0, l0_1, l1_1, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_6], [c0, c1, l1_0, l1_1, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_6], [c0, c1, l1_2, l1_6], [c0, c1, l0_0, l1_2, l1_6], [c0, c1, l0_1, l1_2, l1_6], [c1, l0_0, l0_1, l1_2, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_6], [c0, c1, l1_0, l1_2, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_6], [c0, c1, l1_1, l1_2, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_6], [c0, c1, l1_3, l1_6], [c0, c1, l0_0, l1_3, l1_6], [c0, c1, l0_1, l1_3, l1_6], [c1, l0_0, l0_1, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_3, l1_6], [c0, c1, l1_0, l1_3, l1_6], [c0, c1, l0_0, l1_0, l1_3, l1_6], [c0, c1, l0_1, l1_0, l1_3, l1_6], [c1, l0_0, l0_1, l1_0, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_6], [c0, c1, l1_1, l1_3, l1_6], [c0, c1, l0_0, l1_1, l1_3, l1_6], [c0, c1, l0_1, l1_1, l1_3, l1_6], [c1, l0_0, l0_1, l1_1, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_6], [c0, c1, l1_0, l1_1, l1_3, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_6], [c0, c1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l1_2, l1_3, l1_6], [c0, c1, l0_1, l1_2, l1_3, l1_6], [c1, l0_0, l0_1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_6], [c0, c1, l1_0, l1_2, l1_3, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_6], [c0, c1, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6], [c0, c1, l1_4, l1_6], [c0, c1, l0_0, l1_4, l1_6], [c0, c1, l0_1, l1_4, l1_6], [c1, l0_0, l0_1, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_4, l1_6], [c0, c1, l1_0, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_6], [c0, c1, l1_1, l1_4, l1_6], [c0, c1, l0_0, l1_1, l1_4, l1_6], [c0, c1, l0_1, l1_1, l1_4, l1_6], [c1, l0_0, l0_1, l1_1, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_6], [c0, c1, l1_0, l1_1, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_6], [c0, c1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l1_2, l1_4, l1_6], [c0, c1, l0_1, l1_2, l1_4, l1_6], [c1, l0_0, l0_1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_6], [c0, c1, l1_0, l1_2, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_6], [c0, c1, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6], [c0, c1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_6], [c0, c1, l1_0, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_6], [c0, c1, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_6], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6], [c0, c1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], [c0, c1, l1_5, l1_6], [c0, c1, l0_0, l1_5, l1_6], [c0, c1, l0_1, l1_5, l1_6], [c1, l0_0, l0_1, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_5, l1_6], [c0, c1, l1_0, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_5, l1_6], [c0, c1, l1_1, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_6], [c0, c1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l1_2, l1_5, l1_6], [c0, c1, l0_1, l1_2, l1_5, l1_6], [c1, l0_0, l0_1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_5, l1_6], [c0, c1, l1_0, l1_2, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_6], [c0, c1, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6], [c0, c1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_3, l1_5, l1_6], [c0, c1, l1_0, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_6], [c0, c1, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6], [c0, c1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_2, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l1_0, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6], [c0, c1, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], [c0, c1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_6], [c0, c1, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6], [c0, c1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_2, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6], [c0, c1, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], [c0, c1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [c0, c1, l1_7], [c0, c1, l0_0, l1_7], [c0, c1, l0_1, l1_7], [c1, l0_0, l0_1, l1_7], [c0, c1, l0_0, l0_1, l1_7], [c0, c1, l1_0, l1_7], [c0, c1, l0_0, l1_0, l1_7], [c0, c1, l0_1, l1_0, l1_7], [c1, l0_0, l0_1, l1_0, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_7], [c0, c1, l1_1, l1_7], [c0, c1, l0_0, l1_1, l1_7], [c0, c1, l0_1, l1_1, l1_7], [c1, l0_0, l0_1, l1_1, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_7], [c0, c1, l1_0, l1_1, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_7], [c0, c1, l1_2, l1_7], [c0, c1, l0_0, l1_2, l1_7], [c0, c1, l0_1, l1_2, l1_7], [c1, l0_0, l0_1, l1_2, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_7], [c0, c1, l1_0, l1_2, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_7], [c0, c1, l1_1, l1_2, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_7], [c0, c1, l1_3, l1_7], [c0, c1, l0_0, l1_3, l1_7], [c0, c1, l0_1, l1_3, l1_7], [c1, l0_0, l0_1, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_7], [c0, c1, l1_0, l1_3, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_7], [c0, c1, l1_1, l1_3, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_7], [c0, c1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_7], [c0, c1, l1_4, l1_7], [c0, c1, l0_0, l1_4, l1_7], [c0, c1, l0_1, l1_4, l1_7], [c1, l0_0, l0_1, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_4, l1_7], [c0, c1, l1_0, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_7], [c0, c1, l1_1, l1_4, l1_7], [c0, c1, l0_0, l1_1, l1_4, l1_7], [c0, c1, l0_1, l1_1, l1_4, l1_7], [c1, l0_0, l0_1, l1_1, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_7], [c0, c1, l1_0, l1_1, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_7], [c0, c1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l1_2, l1_4, l1_7], [c0, c1, l0_1, l1_2, l1_4, l1_7], [c1, l0_0, l0_1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_7], [c0, c1, l1_0, l1_2, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_7], [c0, c1, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_7], [c0, c1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_7], [c0, c1, l1_0, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_7], [c0, c1, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_7], [c0, c1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_7], [c0, c1, l1_5, l1_7], [c0, c1, l0_0, l1_5, l1_7], [c0, c1, l0_1, l1_5, l1_7], [c1, l0_0, l0_1, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_5, l1_7], [c0, c1, l1_0, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_5, l1_7], [c0, c1, l1_1, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_7], [c0, c1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l1_2, l1_5, l1_7], [c0, c1, l0_1, l1_2, l1_5, l1_7], [c1, l0_0, l0_1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_5, l1_7], [c0, c1, l1_0, l1_2, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_7], [c0, c1, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_7], [c0, c1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_5, l1_7], [c0, c1, l1_0, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_7], [c0, c1, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_7], [c0, c1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_7], [c0, c1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_7], [c0, c1, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_7], [c0, c1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_2, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_7], [c0, c1, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_7], [c0, c1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], [c0, c1, l1_6, l1_7], [c0, c1, l0_0, l1_6, l1_7], [c0, c1, l0_1, l1_6, l1_7], [c1, l0_0, l0_1, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_6, l1_7], [c0, c1, l1_0, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_6, l1_7], [c0, c1, l1_1, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_6, l1_7], [c0, c1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_6, l1_7], [c0, c1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_6, l1_7], [c0, c1, l1_0, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_6, l1_7], [c0, c1, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_6, l1_7], [c0, c1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_6, l1_7], [c0, c1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_6, l1_7], [c0, c1, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_6, l1_7], [c0, c1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_6, l1_7], [c0, c1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], [c0, c1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_5, l1_6, l1_7], [c0, c1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_5, l1_6, l1_7], [c0, c1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], [c0, c1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [c0, c1, l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7]], [0, 0, 1, 11, 53, 148, 266, 322, 266, 149, 56, 12, 1], 2, [[c0, c1]]]

Conditions: none

Audit every mask against every edge,retaining the first uncovered-edge refutation for each failure and every accepted set in source order.Zero smaller-size counts give a lower bound and actual minimum covers attain it.Keep all ties in numeric-mask order,not English/size order.

Step identifiers and dependenciesRule: Mincover_ALL_masks_acceptance_refutations_ALLcovers_ALLminimizers · Uses: G001, S002





S004 · impliesBefore

source roles = [[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[c0, l0_0], [c0, l0_1], [c1, l1_0], [c1, l1_1], [c1, l1_2], [c1, l1_3], [c1, l1_4], [c1, l1_5], [c1, l1_6], [c1, l1_7]]]

After

derived = [[[[c0, l0_0], Yes], [[c0, l0_1], Yes], [[c1, l1_0], Yes], [[c1, l1_1], Yes], [[c1, l1_2], Yes], [[c1, l1_3], Yes], [[c1, l1_4], Yes], [[c1, l1_5], Yes], [[c1, l1_6], Yes], [[c1, l1_7], Yes]], 10, 2, [c0, c1]]

Conditions: none

First qualify an actual candidate cover.The smaller witness is the first minimum from the complete source list,not an arbitrary small set.

Step identifiers and dependenciesRule: Mincover_actual_candidate_complete_cover_and_smaller_witness · Uses: G001, S003





S005 · impliesBefore

source roles = [[l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], No], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], No], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], No], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], No], [l1_7, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], No]]]

After

derived = [Yes, 2, [c0, c1], No]

Conditions: none

Every single deletion loses coverage,so the candidate is inclusion-minimal.But exhaustive search supplies a strictly smaller cover,so it is not minimum.Superset monotonicity makes deletion tests cover all proper-subset obligations,not maximum or optimal size.

Step identifiers and dependenciesRule: Mincover_ALL_single_deletions_minimal_BUT_smaller_cover_exists · Uses: G001, S004









## Reverse checks


- S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], No], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], No], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], No], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], No], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], No], [l1_7, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], No]], Yes, 2, [c0, c1], No, inclusion_minimal_is_not_minimum)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: 061c2e103b93b7e2c2a2d01e73bb9fb541799c6582b8b8d29d00b5b3218b8850
- candidate record SHA-256: db86af3a161b933ae4224c2fbbe673a96f2deba1ea8dc0a72c33c2b6ff60868d
- semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3
- question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5c
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0067.json)