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------------------------------------------------------------------------
Map identifier: Mp00001

------------------------------------------------------------------------
Map name: to semistandard tableau via monotone triangles

------------------------------------------------------------------------
Domain: Alternating sign matrices

------------------------------------------------------------------------
Codomain: Semistandard tableaux

------------------------------------------------------------------------
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.

------------------------------------------------------------------------
References: [1]   [[AlternatingSignMatrices]]

------------------------------------------------------------------------
Code:

def mapping(elt):
    return elt.to_semistandard_tableau()

------------------------------------------------------------------------
Map images:

[[1]]                                                                                      => [[1]]
[[1,0],[0,1]]                                                                              => [[1,1],[2]]
[[0,1],[1,0]]                                                                              => [[1,2],[2]]
[[1,0,0],[0,1,0],[0,0,1]]                                                                  => [[1,1,1],[2,2],[3]]
[[0,1,0],[1,0,0],[0,0,1]]                                                                  => [[1,1,2],[2,2],[3]]
[[1,0,0],[0,0,1],[0,1,0]]                                                                  => [[1,1,1],[2,3],[3]]
[[0,1,0],[1,-1,1],[0,1,0]]                                                                 => [[1,1,2],[2,3],[3]]
[[0,0,1],[1,0,0],[0,1,0]]                                                                  => [[1,1,3],[2,3],[3]]
[[0,1,0],[0,0,1],[1,0,0]]                                                                  => [[1,2,2],[2,3],[3]]
[[0,0,1],[0,1,0],[1,0,0]]                                                                  => [[1,2,3],[2,3],[3]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,4],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
[[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]]
[[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]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,4],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
[[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]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]                             => [[1,1,1,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]                             => [[1,1,2,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]                             => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]                             => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,5],[5]]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0]]                             => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0]]                             => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                             => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,5],[5]]
[[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]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                            => [[1,1,1,2,4],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                             => [[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,-1,1],[0,0,0,1,0]]                             => [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0]]                             => [[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0]]                             => [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,0,0,1,0]]                             => [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,0,0,1,0]]                            => [[1,1,2,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,-1,1],[0,0,0,1,0]]                             => [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]                             => [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,2],[2,2,2,3],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,3],[2,2,2,3],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,2],[2,2,2,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]                            => [[1,1,1,2,3],[2,2,2,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,4],[2,2,2,4],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,3],[2,2,2,5],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,4],[2,2,2,5],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,2],[2,2,3,3],[3,3,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,2],[2,2,3,3],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,3],[2,2,3,3],[3,3,5],[4,5],[5]]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,1],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,1,2],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,1,3],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,4],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,2,2],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                           => [[1,1,1,2,3],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,2,4],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,3,3],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,3,4],[2,2,3,4],[3,3,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,2],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,3],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,1,4],[2,2,3,5],[3,3,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,2],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,2,3],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                            => [[1,1,1,2,4],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,2,5],[2,2,3,5],[3,3,5],[4,5],[5]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]]                             => [[1,1,1,3,4],[2,2,3,5],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,2,2],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]                            => [[1,1,2,2,3],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,2,4],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,3,3],[2,2,3,4],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,3,4],[2,2,3,4],[3,3,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,2,3],[2,2,3,5],[3,3,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,2,4],[2,2,3,5],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]]                             => [[1,1,2,3,4],[2,2,3,5],[3,3,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,2,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,2,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,2,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,2,2],[2,2,2,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,2,3],[2,2,2,3],[3,4,4],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,2],[2,2,2,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,2,4],[3,4,4],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]                             => [[1,1,1,2,3],[2,2,2,4],[3,4,4],[4,5],[5]]
[[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]]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,2,2],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,2,3],[2,2,3,3],[3,4,4],[4,5],[5]]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,1,3],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,1,4],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,2,2],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                           => [[1,1,1,2,3],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                            => [[1,1,1,2,4],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,3,3],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0]]                             => [[1,1,1,3,4],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,2,2],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,2,3],[2,2,3,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,2,2],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0]]                            => [[1,1,2,2,3],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,2,4],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,3,3],[2,2,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,1,0,0]]                             => [[1,1,2,3,4],[2,2,3,4],[3,4,4],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,2,3],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,2,2],[2,2,2,3],[3,4,5],[4,5],[5]]
[[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]]
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,3],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,4],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,2,2],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                            => [[1,1,1,2,3],[2,2,2,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,2,4],[2,2,2,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,2],[2,2,2,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,2,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,4],[2,2,2,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,2,3],[2,2,2,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]                             => [[1,1,1,2,4],[2,2,2,5],[3,4,5],[4,5],[5]]
[[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]]
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,2,2],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,2,3],[2,2,3,3],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                           => [[1,1,1,1,3],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,4],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                           => [[1,1,1,2,2],[2,2,3,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                           => [[1,1,1,2,4],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,3,3],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,1],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,2],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,3],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,1,4],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,1,5],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,2,2],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                           => [[1,1,1,2,3],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                           => [[1,1,1,2,4],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,2,5],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,3,3],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                            => [[1,1,1,3,4],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]]                             => [[1,1,1,3,5],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,2,2],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,2,3],[2,2,3,3],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,2,2],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]                           => [[1,1,2,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,2,4],[2,2,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,3,3],[2,2,3,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,2,2],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,2,3],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,2,4],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,2,5],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,3,3],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                            => [[1,1,2,3,4],[2,2,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0]]                             => [[1,1,2,3,5],[2,2,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,1,2],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]                            => [[1,1,1,2,3],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,-1,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,3,3],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,-1,0,1],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,3,4],[2,2,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,1,2],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,1,3],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,1,4],[2,2,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,2,2],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                            => [[1,1,1,2,3],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                            => [[1,1,1,2,4],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,2,5],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,3,3],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0]]                            => [[1,1,1,3,4],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0]]                             => [[1,1,1,3,5],[2,2,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,2,3],[2,2,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,-1,0,1],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,3,3],[2,2,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,3,4],[2,2,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,2,3],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,2,4],[2,2,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,3,3],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0]]                            => [[1,1,2,3,4],[2,2,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0]]                             => [[1,1,2,3,5],[2,2,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,1,2],[2,3,3,3],[3,4,4],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,3,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,2,3],[2,3,3,3],[3,4,4],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,1,2],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,1,3],[2,3,3,4],[3,4,4],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]                            => [[1,1,1,2,3],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]                             => [[1,1,1,2,4],[2,3,3,4],[3,4,4],[4,5],[5]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,3,3],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,2,3],[2,3,3,3],[3,4,4],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0]]                            => [[1,1,2,2,3],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,2,4],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,3,3],[2,3,3,4],[3,4,4],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0]]                             => [[1,1,2,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,2],[2,3,3,3],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,3,3],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,2,3],[2,3,3,3],[3,4,5],[4,5],[5]]
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,1],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,1,2],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,1,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,2,2],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                           => [[1,1,1,2,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,2,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,3,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,3,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,2],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,3],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,1,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,2,3],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                            => [[1,1,1,2,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,2,5],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]                             => [[1,1,1,3,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,3,3],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,2,3],[2,3,3,3],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,2,2],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[1,-1,0,1,0],[0,1,0,0,0]]                           => [[1,1,2,2,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,2,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,3,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,3,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,2,3],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,2,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,2,5],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,3,3],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                            => [[1,1,2,3,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]]                             => [[1,1,2,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,1,2],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,1,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]                            => [[1,1,1,2,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,2,4],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,3,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,3,4],[2,3,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,1,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,1,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,2,2],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]                            => [[1,1,1,2,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,2,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,3,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]]                            => [[1,1,1,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]]                             => [[1,1,1,3,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,2,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,2,4],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,3,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,3,4],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,2,2],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,2,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,2,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,3,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]                            => [[1,1,2,3,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0]]                             => [[1,1,2,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]]                             => [[1,1,3,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]]                             => [[1,2,2,2,3],[2,3,3,4],[3,4,4],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,2,2],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0],[1,0,0,0,0]]                            => [[1,2,2,2,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,2,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,3,3],[2,3,3,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,3,4],[2,3,3,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,2,3],[2,3,3,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,2,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]]                             => [[1,2,2,3,4],[2,3,3,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,2,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,0,0,1,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,3,3],[2,3,4,4],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,3,4],[2,3,4,4],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,2,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[0,0,1,0,0],[0,0,0,0,1],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,3,3],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0]]                            => [[1,2,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0]]                             => [[1,2,2,3,5],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]]                             => [[1,2,3,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]      => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,3,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,3,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,2],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,2,5],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,3,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,3,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,4,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,4,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,2,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,4,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,2,4,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,3],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,3],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,1],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,2],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,1,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,2],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,1,2,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,3,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,3],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,2],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]   => [[1,1,1,2,2,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,3,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,1],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,2],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,1,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,1,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,2,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,2,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,1,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,1,3,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,4,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,1,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,2,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,2,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,1,2,3,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,4,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,2,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,3,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,3,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,3,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,1,3,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,3,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,4,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,1,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,3,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,3,4],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,3],[2,2,3,3,3],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,2],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,2,2,2,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,3],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,4],[2,2,3,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,3,3],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,4],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,3,5],[2,2,3,3,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,2,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,2,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]    => [[1,1,2,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,2,3,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,4,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,2,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,3,3,3],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,3,3,4],[2,2,3,4,4],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,3,3,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]     => [[1,1,2,3,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,3,3,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]      => [[1,1,2,3,4,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,0,1,0,0],[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]]      => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,0,1,0,0],[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]]      => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[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]]
[[0,0,0,1,0,0],[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]]     => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]      => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,3,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,3,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,2],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,3,3],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,4],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,3,5],[2,2,2,3,5],[3,3,3,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[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]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,2,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,2],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,2,5],[2,2,2,2,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[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]]
[[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]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,1,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[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]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,3,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,1],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,1,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,1,2,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,3,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,3,3],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]  => [[1,1,1,2,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,3,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[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]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,2],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,2,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,3,4],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,5],[2,2,2,3,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,2,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,1,3,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,3,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,4,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,4,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,2],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,4],[2,2,2,4,4],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,2],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,2,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,2,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,3],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]   => [[1,1,1,2,3,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,2,3,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,4,4],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,2,4,5],[2,2,2,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,2],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,2,3],[2,2,3,3,3],[3,3,4,4],[4,4,5],[5,6],[6]]
[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]     => [[1,1,1,1,1,1],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,2],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]
[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]    => [[1,1,1,1,1,3],[2,2,3,3,4],[3,3,4,4],[4,4,5],[5,6],[6]]

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Created: Jan 01, 2018 at 00:00 by FindStatCrew

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Last Updated: Dec 31, 2019 at 17:32 by Martin Rubey