- FindStat

Identifier

Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 357 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The number of simple modules in

$eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ .

Map

Inverse Kreweras complement

Description

Sends the permutation

$\pi \in \mathfrak{S}_n$ to the permutation

$c\pi^{-1}$ where

$c = (1,\ldots,n)$ is the long cycle.

Map

to left key permutation

Description

Return the permutation of the left key of an alternating sign matrix.
This was originally defined by Lascoux and then further studied by Aval [1].

Map

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let

$(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are

$c_1, c_1+c_2, \dots, c_1+\dots+c_k$ .
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.