Identifier
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Images
[[1]] => [[1]] => [1]
[[1,0],[0,1]] => [[1,1],[2]] => [2,1]
[[0,1],[1,0]] => [[1,2],[2]] => [2,1]
[[1,0,0],[0,1,0],[0,0,1]] => [[1,1,1],[2,2],[3]] => [3,2,1]
[[0,1,0],[1,0,0],[0,0,1]] => [[1,1,2],[2,2],[3]] => [3,2,1]
[[1,0,0],[0,0,1],[0,1,0]] => [[1,1,1],[2,3],[3]] => [3,2,1]
[[0,1,0],[1,-1,1],[0,1,0]] => [[1,1,2],[2,3],[3]] => [2,2,2]
[[0,0,1],[1,0,0],[0,1,0]] => [[1,1,3],[2,3],[3]] => [3,2,1]
[[0,1,0],[0,0,1],[1,0,0]] => [[1,2,2],[2,3],[3]] => [3,2,1]
[[0,0,1],[0,1,0],[1,0,0]] => [[1,2,3],[2,3],[3]] => [3,2,1]
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1]
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1]
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1]
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]] => [[1,1,1,2],[2,2,3],[3,3],[4]] => [3,3,3,1]
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]] => [[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]] => [[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1]
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => [[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1]
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => [[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1]
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]] => [[1,1,1,1],[2,2,3],[3,4],[4]] => [4,2,2,2]
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]] => [[1,1,1,2],[2,2,3],[3,4],[4]] => [3,3,2,2]
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]] => [[1,1,1,3],[2,2,3],[3,4],[4]] => [3,3,2,2]
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]] => [[1,1,2,2],[2,2,3],[3,4],[4]] => [4,2,2,2]
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]] => [[1,1,2,3],[2,2,3],[3,4],[4]] => [3,3,2,2]
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]] => [[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]] => [[1,1,1,2],[2,2,4],[3,4],[4]] => [3,3,3,1]
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]] => [[1,1,1,3],[2,2,4],[3,4],[4]] => [3,3,2,2]
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => [[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]] => [[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1]
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]] => [[1,1,2,3],[2,2,4],[3,4],[4]] => [3,3,2,2]
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]] => [[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1]
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]] => [[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]] => [[1,1,1,2],[2,3,3],[3,4],[4]] => [3,3,2,2]
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]] => [[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]] => [[1,1,2,2],[2,3,3],[3,4],[4]] => [3,3,2,2]
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]] => [[1,1,2,3],[2,3,3],[3,4],[4]] => [4,2,2,2]
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => [[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]] => [[1,1,1,2],[2,3,4],[3,4],[4]] => [3,3,2,2]
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]] => [[1,1,1,3],[2,3,4],[3,4],[4]] => [3,3,3,1]
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]] => [[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]] => [[1,1,2,2],[2,3,4],[3,4],[4]] => [3,3,2,2]
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => [[1,1,2,3],[2,3,4],[3,4],[4]] => [3,3,2,2]
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]] => [[1,1,2,4],[2,3,4],[3,4],[4]] => [4,2,2,2]
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]] => [[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]] => [[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] => [[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1]
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]] => [[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1]
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]] => [[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]] => [[1,2,2,3],[2,3,4],[3,4],[4]] => [3,3,3,1]
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]] => [[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]] => [[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => [[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]] => [4,4,4,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]] => [5,3,3,3,1]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]] => [4,4,4,2,1]
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]] => [4,4,3,3,1]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]] => [4,4,4,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]] => [5,4,2,2,2]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]] => [5,4,2,2,2]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,5],[5]] => [4,3,3,3,2]
>>> Load all 448 entries. <<<
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]] => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]] => [4,3,3,3,2]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]] => [4,3,3,3,2]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]] => [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]] => [4,4,3,2,2]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,3],[3,3,5],[4,5],[5]] => [5,3,3,3,1]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,3],[3,3,5],[4,5],[5]] => [4,4,3,3,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,3],[3,3,5],[4,5],[5]] => [4,4,3,3,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,4],[3,3,5],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,4],[3,3,5],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,4],[3,3,5],[4,5],[5]] => [4,3,3,3,2]
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,4],[2,2,2,4],[3,3,5],[4,5],[5]] => [4,3,3,3,2]
[[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,5],[3,3,5],[4,5],[5]] => [4,4,4,2,1]
[[0,0,1,0,0],[1,0,-1,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,2,5],[3,3,5],[4,5],[5]] => [4,4,3,3,1]
[[0,0,0,1,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,4],[2,2,2,5],[3,3,5],[4,5],[5]] => [4,4,3,2,2]
[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,2,2],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,2,5],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,3,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,2],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,3],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,2],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,3,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,4],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,2,2],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,2,4],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]] => [4,3,3,3,2]
[[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,5],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,2,2],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,2,5],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]] => [5,3,3,2,2]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]] => [4,3,3,3,2]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]] => [3,3,3,3,3]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]] => [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]] => [4,3,3,3,2]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,4,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,2],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,3],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]] => [4,4,3,2,2]
[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]] => [4,3,3,3,2]
[[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [4,4,3,2,2]
[[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,3],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,3,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,3],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,3,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,4,4,4,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => [6,5,3,3,3,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => [6,5,3,3,3,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,4,4,4,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,4,4,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => [4,4,4,4,4,1]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => [5,5,4,3,3,1]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,4,4,4,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => [6,5,4,2,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => [6,5,4,2,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => [6,5,4,2,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => [5,5,5,2,2,2]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => [6,5,4,2,2,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => [6,5,4,2,2,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,4,4,4,2,2]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,4,4,4,2,2]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,4,4,4,2,2]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,5,3,3,3,2]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,4,4,4,2,2]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,5,3,3,3,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => [4,4,4,4,3,2]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => [4,4,4,4,3,2]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]] => [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => [6,5,3,3,3,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => [6,5,3,3,3,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,5,3,3,3,2]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,5,3,3,3,2]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,4,3,3,3,3]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,4,4,4,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,4,2,1]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,4,4,3,3,1]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,4,4,4,3,1]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,4,4,4,3,1]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,4,4,4,2,2]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,3],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,4,2,1]
[[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,4],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,3,3,1]
[[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,5],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,6],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => [5,5,5,3,2,1]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => [5,5,4,3,2,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]] => [6,5,3,3,2,2]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]] => [6,5,3,3,2,2]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => [5,5,3,3,3,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => [6,3,3,3,3,3]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => [5,4,3,3,3,3]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => [5,4,3,3,3,3]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]] => [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,2],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,2,3],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,1],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,4,3,3,3,2]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,2],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,2,3],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,2,3,4],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,1],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,4,4,3,2,2]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,1,2],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,1,2,3],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [[1,1,1,2,3,4],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => [4,4,4,3,3,3]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0]] => [[1,1,2,3,4,5],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [[1,1,1,1,1,1],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
[[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [[1,1,1,1,1,2],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [[1,1,1,1,2,3],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [[1,1,1,2,3,4],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,4,4,3,3,2]
[[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0]] => [[1,1,2,3,4,5],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [5,5,4,3,2,2]
[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => [[1,2,3,4,5,6],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => [6,5,4,3,2,1]
Map
to semistandard tableau via monotone triangles
Description
The semistandard tableau corresponding the monotone triangle of an alternating sign matrix.
This is obtained by interpreting each row of the monotone triangle as an integer partition, and filling the cells of the smallest partition with ones, the second smallest with twos, and so on.
Map
weight
Description
The weight of a semistandard tableau as an integer partition.
The weight (or content) of a semistandard tableaux $T$ with maximal entry $m$ is the weak composition $(\alpha_1, \dots, \alpha_m)$ such that $\alpha_i$ is the number of letters $i$ occurring in $T$.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.