- FindStat

Identifier

Mp00078: Gelfand-Tsetlin patterns —Schuetzenberger involution⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions

Images

[[1,0],[0]] => [[1,0],[1]] => [[1]] => [1]

[[1,0],[1]] => [[1,0],[0]] => [[2]] => [1]

[[2,0],[0]] => [[2,0],[2]] => [[1,1]] => [2]

[[2,0],[1]] => [[2,0],[1]] => [[1,2]] => [2]

[[2,0],[2]] => [[2,0],[0]] => [[2,2]] => [2]

[[1,1],[1]] => [[1,1],[1]] => [[1],[2]] => [1,1]

[[1,0,0],[0,0],[0]] => [[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0],[1,0],[0]] => [[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0],[1,0],[1]] => [[1,0,0],[0,0],[0]] => [[3]] => [1]

[[3,0],[0]] => [[3,0],[3]] => [[1,1,1]] => [3]

[[3,0],[1]] => [[3,0],[2]] => [[1,1,2]] => [3]

[[3,0],[2]] => [[3,0],[1]] => [[1,2,2]] => [3]

[[3,0],[3]] => [[3,0],[0]] => [[2,2,2]] => [3]

[[2,1],[1]] => [[2,1],[2]] => [[1,1],[2]] => [2,1]

[[2,1],[2]] => [[2,1],[1]] => [[1,2],[2]] => [2,1]

[[2,0,0],[0,0],[0]] => [[2,0,0],[2,0],[2]] => [[1,1]] => [2]

[[2,0,0],[1,0],[0]] => [[2,0,0],[2,0],[1]] => [[1,2]] => [2]

[[2,0,0],[1,0],[1]] => [[2,0,0],[1,0],[1]] => [[1,3]] => [2]

[[2,0,0],[2,0],[0]] => [[2,0,0],[2,0],[0]] => [[2,2]] => [2]

[[2,0,0],[2,0],[1]] => [[2,0,0],[1,0],[0]] => [[2,3]] => [2]

[[2,0,0],[2,0],[2]] => [[2,0,0],[0,0],[0]] => [[3,3]] => [2]

[[1,1,0],[1,0],[0]] => [[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1]

[[1,1,0],[1,0],[1]] => [[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1]

[[1,1,0],[1,1],[1]] => [[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1]

[[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1]

[[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1]

[[4,0],[0]] => [[4,0],[4]] => [[1,1,1,1]] => [4]

[[4,0],[1]] => [[4,0],[3]] => [[1,1,1,2]] => [4]

[[4,0],[2]] => [[4,0],[2]] => [[1,1,2,2]] => [4]

[[4,0],[3]] => [[4,0],[1]] => [[1,2,2,2]] => [4]

[[4,0],[4]] => [[4,0],[0]] => [[2,2,2,2]] => [4]

[[3,1],[1]] => [[3,1],[3]] => [[1,1,1],[2]] => [3,1]

[[3,1],[2]] => [[3,1],[2]] => [[1,1,2],[2]] => [3,1]

[[3,1],[3]] => [[3,1],[1]] => [[1,2,2],[2]] => [3,1]

[[2,2],[2]] => [[2,2],[2]] => [[1,1],[2,2]] => [2,2]

[[3,0,0],[0,0],[0]] => [[3,0,0],[3,0],[3]] => [[1,1,1]] => [3]

[[3,0,0],[1,0],[0]] => [[3,0,0],[3,0],[2]] => [[1,1,2]] => [3]

[[3,0,0],[1,0],[1]] => [[3,0,0],[2,0],[2]] => [[1,1,3]] => [3]

[[3,0,0],[2,0],[0]] => [[3,0,0],[3,0],[1]] => [[1,2,2]] => [3]

[[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]] => [[1,2,3]] => [3]

[[3,0,0],[2,0],[2]] => [[3,0,0],[1,0],[1]] => [[1,3,3]] => [3]

[[3,0,0],[3,0],[0]] => [[3,0,0],[3,0],[0]] => [[2,2,2]] => [3]

[[3,0,0],[3,0],[1]] => [[3,0,0],[2,0],[0]] => [[2,2,3]] => [3]

[[3,0,0],[3,0],[2]] => [[3,0,0],[1,0],[0]] => [[2,3,3]] => [3]

[[3,0,0],[3,0],[3]] => [[3,0,0],[0,0],[0]] => [[3,3,3]] => [3]

[[2,1,0],[1,0],[0]] => [[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1]

[[2,1,0],[1,0],[1]] => [[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1]

[[2,1,0],[1,1],[1]] => [[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1]

[[2,1,0],[2,0],[0]] => [[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1]

[[2,1,0],[2,0],[1]] => [[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1]

[[2,1,0],[2,0],[2]] => [[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1]

[[2,1,0],[2,1],[1]] => [[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1]

[[2,1,0],[2,1],[2]] => [[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1]

[[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1]

[[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2]

[[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2]

[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2]

[[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2]

[[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2]

[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2]

[[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2]

[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2]

[[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2]

[[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2]

[[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1]

[[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1]

[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1]

[[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1]

[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1]

[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1]

[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1]

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1]

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1]

[[5,0],[0]] => [[5,0],[5]] => [[1,1,1,1,1]] => [5]

[[5,0],[1]] => [[5,0],[4]] => [[1,1,1,1,2]] => [5]

[[5,0],[2]] => [[5,0],[3]] => [[1,1,1,2,2]] => [5]

[[5,0],[3]] => [[5,0],[2]] => [[1,1,2,2,2]] => [5]

[[5,0],[4]] => [[5,0],[1]] => [[1,2,2,2,2]] => [5]

[[5,0],[5]] => [[5,0],[0]] => [[2,2,2,2,2]] => [5]

[[4,1],[1]] => [[4,1],[4]] => [[1,1,1,1],[2]] => [4,1]

[[4,1],[2]] => [[4,1],[3]] => [[1,1,1,2],[2]] => [4,1]

[[4,1],[3]] => [[4,1],[2]] => [[1,1,2,2],[2]] => [4,1]

[[4,1],[4]] => [[4,1],[1]] => [[1,2,2,2],[2]] => [4,1]

[[3,2],[2]] => [[3,2],[3]] => [[1,1,1],[2,2]] => [3,2]

[[3,2],[3]] => [[3,2],[2]] => [[1,1,2],[2,2]] => [3,2]

[[4,0,0],[0,0],[0]] => [[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4]

[[4,0,0],[1,0],[0]] => [[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4]

[[4,0,0],[1,0],[1]] => [[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4]

[[4,0,0],[2,0],[0]] => [[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4]

[[4,0,0],[2,0],[1]] => [[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4]

[[4,0,0],[2,0],[2]] => [[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4]

[[4,0,0],[3,0],[0]] => [[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4]

[[4,0,0],[3,0],[1]] => [[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4]

[[4,0,0],[3,0],[2]] => [[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4]

[[4,0,0],[3,0],[3]] => [[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4]

[[4,0,0],[4,0],[0]] => [[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4]

[[4,0,0],[4,0],[1]] => [[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4]

>>> Load all 1536 entries. <<<

[[4,0,0],[4,0],[2]] => [[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4]

[[4,0,0],[4,0],[3]] => [[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4]

[[4,0,0],[4,0],[4]] => [[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4]

[[3,1,0],[1,0],[0]] => [[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1]

[[3,1,0],[1,0],[1]] => [[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1]

[[3,1,0],[1,1],[1]] => [[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1]

[[3,1,0],[2,0],[0]] => [[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1]

[[3,1,0],[2,0],[1]] => [[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1]

[[3,1,0],[2,0],[2]] => [[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1]

[[3,1,0],[2,1],[1]] => [[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1]

[[3,1,0],[2,1],[2]] => [[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1]

[[3,1,0],[3,0],[0]] => [[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1]

[[3,1,0],[3,0],[1]] => [[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1]

[[3,1,0],[3,0],[2]] => [[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1]

[[3,1,0],[3,0],[3]] => [[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1]

[[3,1,0],[3,1],[1]] => [[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1]

[[3,1,0],[3,1],[2]] => [[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1]

[[3,1,0],[3,1],[3]] => [[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1]

[[2,2,0],[2,0],[0]] => [[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2]

[[2,2,0],[2,0],[1]] => [[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2]

[[2,2,0],[2,0],[2]] => [[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2]

[[2,2,0],[2,1],[1]] => [[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2]

[[2,2,0],[2,1],[2]] => [[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2]

[[2,2,0],[2,2],[2]] => [[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2]

[[2,1,1],[1,1],[1]] => [[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1]

[[2,1,1],[2,1],[1]] => [[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1]

[[2,1,1],[2,1],[2]] => [[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1]

[[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3]

[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3]

[[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3]

[[3,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3]

[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3]

[[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3]

[[3,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3]

[[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3]

[[3,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3]

[[3,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3]

[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3]

[[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3]

[[3,0,0,0],[3,0,0],[1,0],[1]] => [[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3]

[[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3]

[[3,0,0,0],[3,0,0],[2,0],[1]] => [[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3]

[[3,0,0,0],[3,0,0],[2,0],[2]] => [[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3]

[[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3]

[[3,0,0,0],[3,0,0],[3,0],[1]] => [[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3]

[[3,0,0,0],[3,0,0],[3,0],[2]] => [[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3]

[[3,0,0,0],[3,0,0],[3,0],[3]] => [[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3]

[[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1]

[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1]

[[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1]

[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1]

[[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1]

[[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1]

[[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1]

[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1]

[[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1]

[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1]

[[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1]

[[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1]

[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1]

[[2,1,0,0],[2,1,0],[1,0],[1]] => [[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1]

[[2,1,0,0],[2,1,0],[1,1],[1]] => [[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1]

[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1]

[[2,1,0,0],[2,1,0],[2,0],[1]] => [[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1]

[[2,1,0,0],[2,1,0],[2,0],[2]] => [[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1]

[[2,1,0,0],[2,1,0],[2,1],[1]] => [[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1]

[[2,1,0,0],[2,1,0],[2,1],[2]] => [[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1]

[[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1]

[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1]

[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1]

[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1]

[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2]

[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2]

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2]

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2]

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2]

[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2]

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2]

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2]

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2]

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2]

[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1]

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1]

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1]

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1]

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1]

[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1]

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1]

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1]

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1]

[[6,0],[1]] => [[6,0],[5]] => [[1,1,1,1,1,2]] => [6]

[[6,0],[2]] => [[6,0],[4]] => [[1,1,1,1,2,2]] => [6]

[[6,0],[3]] => [[6,0],[3]] => [[1,1,1,2,2,2]] => [6]

[[6,0],[4]] => [[6,0],[2]] => [[1,1,2,2,2,2]] => [6]

[[6,0],[5]] => [[6,0],[1]] => [[1,2,2,2,2,2]] => [6]

[[6,0],[6]] => [[6,0],[0]] => [[2,2,2,2,2,2]] => [6]

[[5,1],[1]] => [[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1]

[[5,1],[2]] => [[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1]

[[5,1],[3]] => [[5,1],[3]] => [[1,1,1,2,2],[2]] => [5,1]

[[5,1],[4]] => [[5,1],[2]] => [[1,1,2,2,2],[2]] => [5,1]

[[5,1],[5]] => [[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1]

[[4,2],[2]] => [[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2]

[[4,2],[3]] => [[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,2]

[[4,2],[4]] => [[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2]

[[3,3],[3]] => [[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3]

[[5,0,0],[0,0],[0]] => [[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5]

[[5,0,0],[1,0],[0]] => [[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [5]

[[5,0,0],[1,0],[1]] => [[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [5]

[[5,0,0],[2,0],[0]] => [[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [5]

[[5,0,0],[2,0],[1]] => [[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [5]

[[5,0,0],[2,0],[2]] => [[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [5]

[[5,0,0],[3,0],[0]] => [[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [5]

[[5,0,0],[3,0],[1]] => [[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [5]

[[5,0,0],[3,0],[2]] => [[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [5]

[[5,0,0],[3,0],[3]] => [[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [5]

[[5,0,0],[4,0],[0]] => [[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [5]

[[5,0,0],[4,0],[1]] => [[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [5]

[[5,0,0],[4,0],[2]] => [[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [5]

[[5,0,0],[4,0],[3]] => [[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [5]

[[5,0,0],[4,0],[4]] => [[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [5]

[[5,0,0],[5,0],[0]] => [[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5]

[[5,0,0],[5,0],[1]] => [[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [5]

[[5,0,0],[5,0],[2]] => [[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [5]

[[5,0,0],[5,0],[3]] => [[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [5]

[[5,0,0],[5,0],[4]] => [[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [5]

[[5,0,0],[5,0],[5]] => [[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5]

[[4,1,0],[1,0],[0]] => [[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1]

[[4,1,0],[1,0],[1]] => [[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1]

[[4,1,0],[1,1],[1]] => [[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [4,1]

[[4,1,0],[2,0],[0]] => [[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1]

[[4,1,0],[2,0],[1]] => [[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1]

[[4,1,0],[2,0],[2]] => [[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1]

[[4,1,0],[2,1],[1]] => [[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [4,1]

[[4,1,0],[2,1],[2]] => [[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1]

[[4,1,0],[3,0],[0]] => [[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [4,1]

[[4,1,0],[3,0],[1]] => [[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [4,1]

[[4,1,0],[3,0],[2]] => [[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [4,1]

[[4,1,0],[3,0],[3]] => [[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [4,1]

[[4,1,0],[3,1],[1]] => [[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [4,1]

[[4,1,0],[3,1],[2]] => [[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1]

[[4,1,0],[3,1],[3]] => [[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [4,1]

[[4,1,0],[4,0],[0]] => [[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1]

[[4,1,0],[4,0],[1]] => [[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [4,1]

[[4,1,0],[4,0],[2]] => [[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [4,1]

[[4,1,0],[4,0],[3]] => [[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [4,1]

[[4,1,0],[4,0],[4]] => [[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1]

[[4,1,0],[4,1],[1]] => [[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1]

[[4,1,0],[4,1],[2]] => [[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1]

[[4,1,0],[4,1],[3]] => [[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [4,1]

[[4,1,0],[4,1],[4]] => [[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1]

[[3,2,0],[2,0],[0]] => [[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2]

[[3,2,0],[2,0],[1]] => [[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,2]

[[3,2,0],[2,0],[2]] => [[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2]

[[3,2,0],[2,1],[1]] => [[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,2]

[[3,2,0],[2,1],[2]] => [[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [3,2]

[[3,2,0],[2,2],[2]] => [[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [3,2]

[[3,2,0],[3,0],[0]] => [[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2]

[[3,2,0],[3,0],[1]] => [[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,2]

[[3,2,0],[3,0],[2]] => [[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,2]

[[3,2,0],[3,0],[3]] => [[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2]

[[3,2,0],[3,1],[1]] => [[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,2]

[[3,2,0],[3,1],[2]] => [[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [3,2]

[[3,2,0],[3,1],[3]] => [[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,2]

[[3,2,0],[3,2],[2]] => [[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2]

[[3,2,0],[3,2],[3]] => [[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2]

[[3,1,1],[1,1],[1]] => [[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1]

[[3,1,1],[2,1],[1]] => [[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1]

[[3,1,1],[2,1],[2]] => [[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1]

[[3,1,1],[3,1],[1]] => [[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1]

[[3,1,1],[3,1],[2]] => [[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1]

[[3,1,1],[3,1],[3]] => [[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1]

[[2,2,1],[2,1],[1]] => [[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1]

[[2,2,1],[2,1],[2]] => [[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1]

[[2,2,1],[2,2],[2]] => [[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1]

[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4]

[[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4]

[[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4]

[[4,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [4]

[[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4]

[[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4]

[[4,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [4]

[[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4]

[[4,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [4]

[[4,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [4]

[[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4]

[[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4]

[[4,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [4]

[[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4]

[[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [4]

[[4,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [4]

[[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4]

[[4,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [4]

[[4,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [4]

[[4,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [4]

[[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4]

[[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4]

[[4,0,0,0],[4,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [4]

[[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4]

[[4,0,0,0],[4,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [4]

[[4,0,0,0],[4,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [4]

[[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4]

[[4,0,0,0],[4,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [4]

[[4,0,0,0],[4,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [4]

[[4,0,0,0],[4,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [4]

[[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4]

[[4,0,0,0],[4,0,0],[4,0],[1]] => [[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [4]

[[4,0,0,0],[4,0,0],[4,0],[2]] => [[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [4]

[[4,0,0,0],[4,0,0],[4,0],[3]] => [[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [4]

[[4,0,0,0],[4,0,0],[4,0],[4]] => [[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4]

[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1]

[[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1]

[[3,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1]

[[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1]

[[3,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [3,1]

[[3,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [3,1]

[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1]

[[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1]

[[3,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1]

[[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1]

[[3,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1]

[[3,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1]

[[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1]

[[3,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [3,1]

[[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [3,1]

[[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1]

[[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1]

[[3,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1]

[[3,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [3,1]

[[3,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1]

[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [3,1]

[[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1]

[[3,1,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [3,1]

[[3,1,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [3,1]

[[3,1,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [3,1]

[[3,1,0,0],[3,1,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[3,1],[1]] => [[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[3,1],[2]] => [[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1]

[[3,1,0,0],[3,1,0],[3,1],[3]] => [[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1]

[[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2]

[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2]

[[2,2,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2]

[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2]

[[2,2,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2]

[[2,2,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2]

[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2]

[[2,2,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2]

[[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2]

[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2]

[[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2]

[[2,2,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2]

[[2,2,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2]

[[2,2,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2]

[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2]

[[2,2,0,0],[2,2,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2]

[[2,2,0,0],[2,2,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2]

[[2,2,0,0],[2,2,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2]

[[2,2,0,0],[2,2,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2]

[[2,2,0,0],[2,2,0],[2,2],[2]] => [[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2]

[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1]

[[2,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1]

[[2,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1]

[[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [2,1,1]

[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1]

[[2,1,1,0],[2,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1]

[[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [2,1,1]

[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1]

[[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [2,1,1]

[[2,1,1,0],[2,1,0],[2,0],[2]] => [[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1]

[[2,1,1,0],[2,1,0],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1]

[[2,1,1,0],[2,1,0],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1]

[[2,1,1,0],[2,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1]

[[2,1,1,0],[2,1,1],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1]

[[2,1,1,0],[2,1,1],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1]

[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1]

[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3]

[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3]

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3]

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3]

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [3]

[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3]

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3]

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3]

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [3]

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3]

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3]

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [3]

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3]

[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1]

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1]

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1]

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [2,1]

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1]

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1]

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1]

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1]

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1]

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1]

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1]

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1]

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1]

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1]

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1]

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1]

[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1]

[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2]

[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2]

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2]

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2]

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2]

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [2]

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2]

[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1]

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1]

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1]

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1]

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1]

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1]

[[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1]

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1]

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1]

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1]

[[7,0],[1]] => [[7,0],[6]] => [[1,1,1,1,1,1,2]] => [7]

[[7,0],[2]] => [[7,0],[5]] => [[1,1,1,1,1,2,2]] => [7]

[[7,0],[3]] => [[7,0],[4]] => [[1,1,1,1,2,2,2]] => [7]

[[7,0],[4]] => [[7,0],[3]] => [[1,1,1,2,2,2,2]] => [7]

[[7,0],[5]] => [[7,0],[2]] => [[1,1,2,2,2,2,2]] => [7]

[[7,0],[6]] => [[7,0],[1]] => [[1,2,2,2,2,2,2]] => [7]

[[7,0],[7]] => [[7,0],[0]] => [[2,2,2,2,2,2,2]] => [7]

[[6,1],[1]] => [[6,1],[6]] => [[1,1,1,1,1,1],[2]] => [6,1]

[[6,1],[2]] => [[6,1],[5]] => [[1,1,1,1,1,2],[2]] => [6,1]

[[6,1],[3]] => [[6,1],[4]] => [[1,1,1,1,2,2],[2]] => [6,1]

[[6,1],[4]] => [[6,1],[3]] => [[1,1,1,2,2,2],[2]] => [6,1]

[[6,1],[5]] => [[6,1],[2]] => [[1,1,2,2,2,2],[2]] => [6,1]

[[6,1],[6]] => [[6,1],[1]] => [[1,2,2,2,2,2],[2]] => [6,1]

[[5,2],[2]] => [[5,2],[5]] => [[1,1,1,1,1],[2,2]] => [5,2]

[[5,2],[3]] => [[5,2],[4]] => [[1,1,1,1,2],[2,2]] => [5,2]

[[5,2],[4]] => [[5,2],[3]] => [[1,1,1,2,2],[2,2]] => [5,2]

[[5,2],[5]] => [[5,2],[2]] => [[1,1,2,2,2],[2,2]] => [5,2]

[[4,3],[3]] => [[4,3],[4]] => [[1,1,1,1],[2,2,2]] => [4,3]

[[4,3],[4]] => [[4,3],[3]] => [[1,1,1,2],[2,2,2]] => [4,3]

[[6,0,0],[1,0],[0]] => [[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [6]

[[6,0,0],[1,0],[1]] => [[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [6]

[[6,0,0],[2,0],[0]] => [[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [6]

[[6,0,0],[2,0],[1]] => [[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [6]

[[6,0,0],[2,0],[2]] => [[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [6]

[[6,0,0],[3,0],[0]] => [[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [6]

[[6,0,0],[3,0],[1]] => [[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [6]

[[6,0,0],[3,0],[2]] => [[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [6]

[[6,0,0],[3,0],[3]] => [[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [6]

[[6,0,0],[4,0],[0]] => [[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [6]

[[6,0,0],[4,0],[1]] => [[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [6]

[[6,0,0],[4,0],[2]] => [[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [6]

[[6,0,0],[4,0],[3]] => [[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [6]

[[6,0,0],[4,0],[4]] => [[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [6]

[[6,0,0],[5,0],[0]] => [[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [6]

[[6,0,0],[5,0],[1]] => [[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [6]

[[6,0,0],[5,0],[2]] => [[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [6]

[[6,0,0],[5,0],[3]] => [[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [6]

[[6,0,0],[5,0],[4]] => [[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [6]

[[6,0,0],[5,0],[5]] => [[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [6]

[[6,0,0],[6,0],[0]] => [[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [6]

[[6,0,0],[6,0],[1]] => [[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [6]

[[6,0,0],[6,0],[2]] => [[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [6]

[[6,0,0],[6,0],[3]] => [[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [6]

[[6,0,0],[6,0],[4]] => [[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [6]

[[6,0,0],[6,0],[5]] => [[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [6]

[[6,0,0],[6,0],[6]] => [[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [6]

[[5,1,0],[1,0],[0]] => [[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1]

[[5,1,0],[1,0],[1]] => [[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]] => [5,1]

[[5,1,0],[1,1],[1]] => [[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]] => [5,1]

[[5,1,0],[2,0],[0]] => [[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1]

[[5,1,0],[2,0],[1]] => [[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]] => [5,1]

[[5,1,0],[2,0],[2]] => [[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]] => [5,1]

[[5,1,0],[2,1],[1]] => [[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]] => [5,1]

[[5,1,0],[2,1],[2]] => [[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]] => [5,1]

[[5,1,0],[3,0],[0]] => [[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]] => [5,1]

[[5,1,0],[3,0],[1]] => [[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]] => [5,1]

[[5,1,0],[3,0],[2]] => [[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]] => [5,1]

[[5,1,0],[3,0],[3]] => [[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]] => [5,1]

[[5,1,0],[3,1],[1]] => [[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]] => [5,1]

[[5,1,0],[3,1],[2]] => [[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]] => [5,1]

[[5,1,0],[3,1],[3]] => [[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]] => [5,1]

[[5,1,0],[4,0],[0]] => [[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]] => [5,1]

[[5,1,0],[4,0],[1]] => [[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]] => [5,1]

[[5,1,0],[4,0],[2]] => [[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]] => [5,1]

[[5,1,0],[4,0],[3]] => [[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]] => [5,1]

[[5,1,0],[4,0],[4]] => [[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]] => [5,1]

[[5,1,0],[4,1],[1]] => [[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]] => [5,1]

[[5,1,0],[4,1],[2]] => [[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]] => [5,1]

[[5,1,0],[4,1],[3]] => [[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]] => [5,1]

[[5,1,0],[4,1],[4]] => [[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]] => [5,1]

[[5,1,0],[5,0],[0]] => [[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1]

[[5,1,0],[5,0],[1]] => [[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]] => [5,1]

[[5,1,0],[5,0],[2]] => [[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]] => [5,1]

[[5,1,0],[5,0],[3]] => [[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]] => [5,1]

[[5,1,0],[5,0],[4]] => [[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]] => [5,1]

[[5,1,0],[5,0],[5]] => [[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]] => [5,1]

[[5,1,0],[5,1],[1]] => [[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]] => [5,1]

[[5,1,0],[5,1],[2]] => [[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]] => [5,1]

[[5,1,0],[5,1],[3]] => [[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]] => [5,1]

[[5,1,0],[5,1],[4]] => [[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]] => [5,1]

[[5,1,0],[5,1],[5]] => [[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]] => [5,1]

[[4,2,0],[2,0],[0]] => [[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2]

[[4,2,0],[2,0],[1]] => [[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]] => [4,2]

[[4,2,0],[2,0],[2]] => [[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]] => [4,2]

[[4,2,0],[2,1],[1]] => [[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]] => [4,2]

[[4,2,0],[2,1],[2]] => [[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]] => [4,2]

[[4,2,0],[2,2],[2]] => [[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]] => [4,2]

[[4,2,0],[3,0],[0]] => [[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,2]

[[4,2,0],[3,0],[1]] => [[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]] => [4,2]

[[4,2,0],[3,0],[2]] => [[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]] => [4,2]

[[4,2,0],[3,0],[3]] => [[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]] => [4,2]

[[4,2,0],[3,1],[1]] => [[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]] => [4,2]

[[4,2,0],[3,1],[2]] => [[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]] => [4,2]

[[4,2,0],[3,1],[3]] => [[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]] => [4,2]

[[4,2,0],[3,2],[2]] => [[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]] => [4,2]

[[4,2,0],[3,2],[3]] => [[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]] => [4,2]

[[4,2,0],[4,0],[0]] => [[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2]

[[4,2,0],[4,0],[1]] => [[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]] => [4,2]

[[4,2,0],[4,0],[2]] => [[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]] => [4,2]

[[4,2,0],[4,0],[3]] => [[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]] => [4,2]

[[4,2,0],[4,0],[4]] => [[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]] => [4,2]

[[4,2,0],[4,1],[1]] => [[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]] => [4,2]

[[4,2,0],[4,1],[2]] => [[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]] => [4,2]

[[4,2,0],[4,1],[3]] => [[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]] => [4,2]

[[4,2,0],[4,1],[4]] => [[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]] => [4,2]

[[4,2,0],[4,2],[2]] => [[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]] => [4,2]

[[4,2,0],[4,2],[3]] => [[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]] => [4,2]

[[4,2,0],[4,2],[4]] => [[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]] => [4,2]

[[4,1,1],[1,1],[1]] => [[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [4,1,1]

[[4,1,1],[2,1],[1]] => [[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [4,1,1]

[[4,1,1],[2,1],[2]] => [[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [4,1,1]

[[4,1,1],[3,1],[1]] => [[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [4,1,1]

[[4,1,1],[3,1],[2]] => [[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [4,1,1]

[[4,1,1],[3,1],[3]] => [[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [4,1,1]

[[4,1,1],[4,1],[1]] => [[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [4,1,1]

[[4,1,1],[4,1],[2]] => [[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [4,1,1]

[[4,1,1],[4,1],[3]] => [[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [4,1,1]

[[4,1,1],[4,1],[4]] => [[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [4,1,1]

[[3,3,0],[3,0],[0]] => [[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3]

[[3,3,0],[3,0],[1]] => [[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [3,3]

[[3,3,0],[3,0],[2]] => [[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [3,3]

[[3,3,0],[3,0],[3]] => [[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [3,3]

[[3,3,0],[3,1],[1]] => [[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,3]

[[3,3,0],[3,1],[2]] => [[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [3,3]

[[3,3,0],[3,1],[3]] => [[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [3,3]

[[3,3,0],[3,2],[2]] => [[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [3,3]

[[3,3,0],[3,2],[3]] => [[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [3,3]

[[3,3,0],[3,3],[3]] => [[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [3,3]

[[3,2,1],[2,1],[1]] => [[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]] => [3,2,1]

[[3,2,1],[2,1],[2]] => [[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]] => [3,2,1]

[[3,2,1],[2,2],[2]] => [[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]] => [3,2,1]

[[3,2,1],[3,1],[1]] => [[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]] => [3,2,1]

[[3,2,1],[3,1],[2]] => [[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]] => [3,2,1]

[[3,2,1],[3,1],[3]] => [[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]] => [3,2,1]

[[3,2,1],[3,2],[2]] => [[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]] => [3,2,1]

[[3,2,1],[3,2],[3]] => [[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]] => [3,2,1]

[[2,2,2],[2,2],[2]] => [[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [2,2,2]

[[5,0,0,0],[0,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5]

[[5,0,0,0],[1,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [5]

[[5,0,0,0],[1,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [5]

[[5,0,0,0],[1,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [5]

[[5,0,0,0],[2,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [5]

[[5,0,0,0],[2,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [5]

[[5,0,0,0],[2,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [5]

[[5,0,0,0],[2,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [5]

[[5,0,0,0],[2,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [5]

[[5,0,0,0],[2,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [5]

[[5,0,0,0],[3,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [5]

[[5,0,0,0],[3,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [5]

[[5,0,0,0],[3,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [5]

[[5,0,0,0],[3,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [5]

[[5,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [5]

[[5,0,0,0],[3,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [5]

[[5,0,0,0],[3,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [5]

[[5,0,0,0],[3,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [5]

[[5,0,0,0],[3,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [5]

[[5,0,0,0],[3,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [5]

[[5,0,0,0],[4,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [5]

[[5,0,0,0],[4,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [5]

[[5,0,0,0],[4,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [5]

[[5,0,0,0],[4,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [5]

[[5,0,0,0],[4,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [5]

[[5,0,0,0],[4,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [5]

[[5,0,0,0],[4,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [5]

[[5,0,0,0],[4,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [5]

[[5,0,0,0],[4,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [5]

[[5,0,0,0],[4,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [5]

[[5,0,0,0],[4,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [5]

[[5,0,0,0],[4,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [5]

[[5,0,0,0],[4,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [5]

[[5,0,0,0],[4,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [5]

[[5,0,0,0],[4,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5]

[[5,0,0,0],[5,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [5]

[[5,0,0,0],[5,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [5]

[[5,0,0,0],[5,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [5]

[[5,0,0,0],[5,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [5]

[[5,0,0,0],[5,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [5]

[[5,0,0,0],[5,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [5]

[[5,0,0,0],[5,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [5]

[[5,0,0,0],[5,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [5]

[[5,0,0,0],[5,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [5]

[[5,0,0,0],[5,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [5]

[[5,0,0,0],[5,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [5]

[[5,0,0,0],[5,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[0]] => [[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[1]] => [[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[2]] => [[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[3]] => [[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[4]] => [[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [5]

[[5,0,0,0],[5,0,0],[5,0],[5]] => [[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [5]

[[4,1,0,0],[1,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1]

[[4,1,0,0],[1,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1]

[[4,1,0,0],[1,0,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => [4,1]

[[4,1,0,0],[1,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [4,1]

[[4,1,0,0],[1,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => [4,1]

[[4,1,0,0],[1,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => [4,1]

[[4,1,0,0],[2,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1]

[[4,1,0,0],[2,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1]

[[4,1,0,0],[2,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => [4,1]

[[4,1,0,0],[2,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1]

[[4,1,0,0],[2,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => [4,1]

[[4,1,0,0],[2,0,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => [4,1]

[[4,1,0,0],[2,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [4,1]

[[4,1,0,0],[2,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => [4,1]

[[4,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => [4,1]

[[4,1,0,0],[2,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1]

[[4,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => [4,1]

[[4,1,0,0],[2,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => [4,1]

[[4,1,0,0],[2,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => [4,1]

[[4,1,0,0],[2,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => [4,1]

[[4,1,0,0],[3,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => [4,1]

[[4,1,0,0],[3,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [4,1]

[[4,1,0,0],[3,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => [4,1]

[[4,1,0,0],[3,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => [4,1]

[[4,1,0,0],[3,0,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => [4,1]

[[4,1,0,0],[3,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => [4,1]

[[4,1,0,0],[3,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => [4,1]

[[4,1,0,0],[4,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[3,0],[3]] => [[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => [4,1]

[[4,1,0,0],[4,0,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1]

[[4,1,0,0],[4,0,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => [4,1]

[[4,1,0,0],[4,0,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => [4,1]

[[4,1,0,0],[4,0,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => [4,1]

[[4,1,0,0],[4,0,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => [4,1]

[[4,1,0,0],[4,1,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[4,1],[1]] => [[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[4,1],[2]] => [[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[4,1],[3]] => [[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => [4,1]

[[4,1,0,0],[4,1,0],[4,1],[4]] => [[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => [4,1]

[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2]

[[3,2,0,0],[2,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,2]

[[3,2,0,0],[2,0,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => [3,2]

[[3,2,0,0],[2,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2]

[[3,2,0,0],[2,0,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => [3,2]

[[3,2,0,0],[2,0,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => [3,2]

[[3,2,0,0],[2,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,2]

[[3,2,0,0],[2,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => [3,2]

[[3,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => [3,2]

[[3,2,0,0],[2,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [3,2]

[[3,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => [3,2]

[[3,2,0,0],[2,1,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => [3,2]

[[3,2,0,0],[2,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => [3,2]

[[3,2,0,0],[2,1,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => [3,2]

[[3,2,0,0],[2,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [3,2]

[[3,2,0,0],[2,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => [3,2]

[[3,2,0,0],[2,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => [3,2]

[[3,2,0,0],[2,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => [3,2]

[[3,2,0,0],[2,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => [3,2]

[[3,2,0,0],[2,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => [3,2]

[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2]

[[3,2,0,0],[3,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,2]

[[3,2,0,0],[3,0,0],[1,0],[1]] => [[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => [3,2]

[[3,2,0,0],[3,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,2]

[[3,2,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => [3,2]

[[3,2,0,0],[3,0,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => [3,2]

[[3,2,0,0],[3,0,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2]

[[3,2,0,0],[3,0,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => [3,2]

[[3,2,0,0],[3,0,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => [3,2]

[[3,2,0,0],[3,0,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => [3,2]

[[3,2,0,0],[3,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,2]

[[3,2,0,0],[3,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => [3,2]

[[3,2,0,0],[3,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => [3,2]

[[3,2,0,0],[3,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [3,2]

[[3,2,0,0],[3,1,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => [3,2]

[[3,2,0,0],[3,1,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => [3,2]

[[3,2,0,0],[3,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => [3,2]

[[3,2,0,0],[3,1,0],[2,1],[2]] => [[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => [3,2]

[[3,2,0,0],[3,1,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,2]

[[3,2,0,0],[3,1,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => [3,2]

[[3,2,0,0],[3,1,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => [3,2]

[[3,2,0,0],[3,1,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => [3,2]

[[3,2,0,0],[3,1,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => [3,2]

[[3,2,0,0],[3,1,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => [3,2]

[[3,2,0,0],[3,1,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2]

[[3,2,0,0],[3,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => [3,2]

[[3,2,0,0],[3,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => [3,2]

[[3,2,0,0],[3,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2]

[[3,2,0,0],[3,2,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => [3,2]

[[3,2,0,0],[3,2,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,2],[2]] => [[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => [3,2]

[[3,2,0,0],[3,2,0],[3,2],[3]] => [[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => [3,2]

[[3,1,1,0],[1,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1]

[[3,1,1,0],[1,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [3,1,1]

[[3,1,1,0],[1,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [3,1,1]

[[3,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [3,1,1]

[[3,1,1,0],[2,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1]

[[3,1,1,0],[2,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [3,1,1]

[[3,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [3,1,1]

[[3,1,1,0],[2,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1]

[[3,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [3,1,1]

[[3,1,1,0],[2,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [3,1,1]

[[3,1,1,0],[2,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [3,1,1]

[[3,1,1,0],[2,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[2,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [3,1,1]

[[3,1,1,0],[2,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [3,1,1]

[[3,1,1,0],[2,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,0],[0]] => [[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,0],[1]] => [[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,0],[2]] => [[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,0],[3]] => [[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,0],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [3,1,1]

[[3,1,1,0],[3,1,1],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,1,1]

[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1]

[[2,2,1,0],[2,1,0],[1,0],[1]] => [[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => [2,2,1]

[[2,2,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => [2,2,1]

[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1]

[[2,2,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => [2,2,1]

[[2,2,1,0],[2,1,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => [2,2,1]

[[2,2,1,0],[2,1,0],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => [2,2,1]

[[2,2,1,0],[2,1,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => [2,2,1]

[[2,2,1,0],[2,1,1],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => [2,2,1]

[[2,2,1,0],[2,1,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => [2,2,1]

[[2,2,1,0],[2,1,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,1],[1]] => [[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => [2,2,1]

[[2,2,1,0],[2,2,0],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => [2,2,1]

[[2,2,1,0],[2,2,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => [2,2,1]

[[2,2,1,0],[2,2,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => [2,2,1]

[[2,2,1,0],[2,2,1],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => [2,2,1]

[[2,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => [2,1,1,1]

[[2,1,1,1],[2,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => [2,1,1,1]

[[2,1,1,1],[2,1,1],[2,1],[1]] => [[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => [2,1,1,1]

[[2,1,1,1],[2,1,1],[2,1],[2]] => [[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => [2,1,1,1]

[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4]

[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [4]

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [4]

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [4]

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [4]

[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [4]

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [4]

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [4]

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [4]

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [4]

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [4]

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [4]

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4]

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [4]

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [4]

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [4]

[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1]

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1]

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1]

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]] => [3,1]

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]] => [3,1]

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]] => [3,1]

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]] => [3,1]

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]] => [3,1]

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]] => [3,1]

[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [2,2]

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,2]

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [2,2]

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [2,2]

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1]

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1]

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]] => [2,1,1]

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]] => [2,1,1]

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]] => [2,1,1]

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1]

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3],[5]] => [1,1,1,1]

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4],[5]] => [1,1,1,1]

[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4],[5]] => [1,1,1,1]

[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4],[5]] => [1,1,1,1]

[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3]

[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [3]

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [3]

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [3]

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [3]

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,6]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,6]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,6]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,6]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,6]] => [3]

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6,6]] => [3]

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6,6]] => [3]

[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1]

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1]

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1]

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1]

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[6]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[6]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[6]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[6]] => [2,1]

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[6]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,6],[2]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,6],[3]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,6],[4]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[5]] => [2,1]

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,6],[3]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,6],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,6],[4]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[5]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5],[6]] => [2,1]

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6],[6]] => [2,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5],[6]] => [1,1,1]

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5],[6]] => [1,1,1]

[[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [2]

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,7]] => [2]

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[7,7]] => [2]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1]

[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[7]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[7]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[7]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[7]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[7]] => [1,1]

[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6],[7]] => [1,1]

[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1]

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1]

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1]

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1]

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1]

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1]

[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => [5]

[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => [4,1]

[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => [4,1]

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => [4,1]

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => [4,1]

[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => [3,2]

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => [3,2]

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => [3,2]

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => [3,2]

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => [3,2]

[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => [3,1,1]

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => [3,1,1]

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => [3,1,1]

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => [3,1,1]

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => [3,1,1]

[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => [3,1,1]

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => [2,2,1]

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => [2,2,1]

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => [2,2,1]

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => [2,2,1]

[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => [2,2,1]

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => [2,1,1,1]

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => [2,1,1,1]

[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => [2,1,1,1]

[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => [2,1,1,1]

[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1]

[[1]] => [[1]] => [[1]] => [1]

[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5,6]] => [6]

[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5],[6]] => [5,1]

[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,6],[5]] => [5,1]

[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5,6],[4]] => [5,1]

[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5,6],[3]] => [5,1]

[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5,6],[2]] => [5,1]

[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4,6]] => [4,2]

[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5,6]] => [4,2]

[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3,6]] => [4,2]

[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3,5]] => [4,2]

[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4,5]] => [4,2]

[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2,6]] => [4,2]

[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2,5]] => [4,2]

[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2,4]] => [4,2]

[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3,4]] => [4,2]

[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5],[6]] => [4,1,1]

[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4],[6]] => [4,1,1]

[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4],[5]] => [4,1,1]

[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3],[6]] => [4,1,1]

[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3],[5]] => [4,1,1]

[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3],[4]] => [4,1,1]

[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2],[6]] => [4,1,1]

[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2],[5]] => [4,1,1]

[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2],[4]] => [4,1,1]

[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5,6],[2],[3]] => [4,1,1]

[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4,6]] => [3,3]

[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5,6]] => [3,3]

[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4,6]] => [3,3]

[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5,6]] => [3,3]

[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5,6]] => [3,3]

[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5],[6]] => [3,2,1]

[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5],[6]] => [3,2,1]

[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,6],[5]] => [3,2,1]

[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,6],[4]] => [3,2,1]

[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,6],[5]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5],[6]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4],[6]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,4],[5]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4],[6]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,4],[5]] => [3,2,1]

[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,5],[4]] => [3,2,1]

[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,6],[4]] => [3,2,1]

[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,6],[5]] => [3,2,1]

[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2,6],[3]] => [3,2,1]

[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2,5],[3]] => [3,2,1]

[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,5],[4]] => [3,2,1]

[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3],[4],[5]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2],[4],[5]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3],[6]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2],[3],[5]] => [3,1,1,1]

[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5,6],[2],[3],[4]] => [3,1,1,1]

[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3,6]] => [2,2,2]

[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4,6]] => [2,2,2]

[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5,6]] => [2,2,2]

[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4,6]] => [2,2,2]

[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5,6]] => [2,2,2]

[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5],[6]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5],[6]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4],[6]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,6],[4],[5]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3],[6]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4],[6]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,6],[4],[5]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2,6],[3],[4]] => [2,2,1,1]

[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,6],[3],[5]] => [2,2,1,1]

[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1]

[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5],[6]] => [2,1,1,1,1]

[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5],[6]] => [2,1,1,1,1]

[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4],[6]] => [2,1,1,1,1]

[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,6],[2],[3],[4],[5]] => [2,1,1,1,1]

[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1]

[[2]] => [[2]] => [[1,1]] => [2]

[[3]] => [[3]] => [[1,1,1]] => [3]

[[4]] => [[4]] => [[1,1,1,1]] => [4]

[[5]] => [[5]] => [[1,1,1,1,1]] => [5]

[[4,3,2,1],[4,3,2],[4,3],[4]] => [[4,3,2,1],[3,2,1],[2,1],[1]] => [[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,2],[4,3],[3]] => [[4,3,2,1],[4,2,1],[2,1],[1]] => [[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,2],[4,2],[4]] => [[4,3,2,1],[3,2,1],[3,1],[1]] => [[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,2],[3,2],[3]] => [[4,3,2,1],[4,2,1],[4,1],[1]] => [[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,2],[4,2],[2]] => [[4,3,2,1],[4,3,1],[3,1],[1]] => [[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,2],[3,2],[2]] => [[4,3,2,1],[4,3,1],[4,1],[1]] => [[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[4,3],[4]] => [[4,3,2,1],[3,2,1],[2,1],[2]] => [[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[4,3],[3]] => [[4,3,2,1],[4,2,1],[2,1],[2]] => [[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[3,2],[3]] => [[4,3,2,1],[4,2,1],[3,2],[2]] => [[1,1,2,3],[2,2,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[4,2],[4]] => [[4,3,2,1],[3,2,1],[3,1],[3]] => [[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[3,2],[3]] => [[4,3,2,1],[4,2,1],[4,1],[4]] => [[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[4,2],[2]] => [[4,3,2,1],[4,3,1],[3,1],[3]] => [[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[3,2],[2]] => [[4,3,2,1],[4,3,1],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[3,2],[2]] => [[4,3,2,1],[4,3,1],[4,1],[4]] => [[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[4,1],[4]] => [[4,3,2,1],[3,2,1],[3,2],[2]] => [[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[3,1],[3]] => [[4,3,2,1],[4,2,1],[4,2],[2]] => [[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[4,1],[4]] => [[4,3,2,1],[3,2,1],[3,2],[3]] => [[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[3,1],[3]] => [[4,3,2,1],[4,2,1],[4,2],[4]] => [[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[2,1],[2]] => [[4,3,2,1],[4,3,1],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[2,1],[2]] => [[4,3,2,1],[4,3,1],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[4,1],[1]] => [[4,3,2,1],[4,3,2],[3,2],[2]] => [[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1]

[[4,3,2,1],[4,3,1],[3,1],[1]] => [[4,3,2,1],[4,3,2],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[4,1],[1]] => [[4,3,2,1],[4,3,2],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[3,1],[1]] => [[4,3,2,1],[4,3,2],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1]

[[4,3,2,1],[4,2,1],[2,1],[1]] => [[4,3,2,1],[4,3,2],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1]

[[4,3,2,1],[3,2,1],[2,1],[1]] => [[4,3,2,1],[4,3,2],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1]

Map

Schuetzenberger involution

Description

Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type $A$ it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than $n$. Use Schuetzenberger's jeu de taquin to slide all entries equal to $1$ to the outer border of the tableau. Do the same for all entries equal to $2$, restricting the tableau to the entries larger than $2$, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to $n$, that is, replace $e$ with $n+1-e$.

Map

to semistandard tableau

Description

Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.

Map

shape

Description

Return the shape of a tableau.