- FindStat

Identifier

Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001630: Lattices ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 1

[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 1

[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2

[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 1

[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2

[1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2

[1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 2

[1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2

[1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

[1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2

[1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,2,7,3,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,2,7,4,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,2,7,4,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,2,7,6,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,2,7,6,4,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,4,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,4,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,3,7,6,4,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,3,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,3,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,5,4,7,6,3,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => 1

[2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

>>> Load all 514 entries. <<<

[2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2

[2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

[2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 1

[2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2

[2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 2

[2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2

[2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2

[2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 1

[2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 1

[2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2

[2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 1

[2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 1

[2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 1

[2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => ([(0,2),(2,1)],3) => 1

[2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => 1

[2,3,5,1,7,6,4] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => 1

[2,3,5,4,6,7,1] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => ([(0,2),(2,1)],3) => 1

[2,3,5,4,7,1,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => 1

[2,3,5,4,7,6,1] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => 1

[2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[2,4,1,5,7,6,3] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,4,1,6,5,7,3] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,4,1,6,7,3,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => 1

[2,4,1,6,7,5,3] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => 1

[2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,1,7,3,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,1,7,5,3,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,1,7,5,6,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,1,7,6,3,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,1,7,6,5,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,5,7,1,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[2,4,3,5,7,6,1] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[2,4,3,6,1,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,4,3,6,5,7,1] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,4,3,6,7,1,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => 1

[2,4,3,6,7,5,1] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => 1

[2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,7,1,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,7,5,1,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,7,6,1,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,3,7,6,5,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,4,5,1,7,3,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,4,5,1,7,6,3] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,4,5,3,7,1,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,4,5,3,7,6,1] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,1,5,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,1,7,5,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,3,1,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,3,7,1,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,3,7,5,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,5,1,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,5,3,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,4,6,5,7,3,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,3,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,4,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,6,4,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,3,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,4,3,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,4,6,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,6,3,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,1,7,6,4,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,1,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,1,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,4,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,4,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,6,1,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,6,4,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,1,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,1,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,4,1,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,4,6,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,6,1,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,3,7,6,4,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,1,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,1,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,3,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,3,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,6,1,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,6,3,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,1,3,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,1,6,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,3,1,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,3,6,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,6,1,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,5,4,7,6,3,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => 1

[3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => ([(0,2),(2,1)],3) => 1

[3,1,4,5,7,6,2] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => ([(0,2),(2,1)],3) => 1

[3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[3,1,4,6,5,7,2] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[3,1,4,6,7,2,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,6,7,5,2] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,1,5,2,7,6,4] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,1,5,4,6,7,2] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,5,4,7,2,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,1,5,4,7,6,2] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,1,5,6,2,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[3,1,5,6,4,7,2] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,2,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,2,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,2,7,5,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,4,2,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,4,5,7,2] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,4,7,2,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,4,7,5,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,5,2,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,5,4,7,2] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,1,6,5,7,2,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,1,6,5,7,4,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,4,5,7,1,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => ([(0,2),(2,1)],3) => 1

[3,2,4,5,7,6,1] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => ([(0,2),(2,1)],3) => 1

[3,2,4,6,1,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[3,2,4,6,5,7,1] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[3,2,4,6,7,1,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,6,7,5,1] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,2,5,1,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,5,1,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,2,5,1,7,6,4] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,2,5,4,6,7,1] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,5,4,7,1,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,2,5,4,7,6,1] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

[3,2,5,6,1,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[3,2,5,6,4,7,1] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,1,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,1,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,1,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,1,7,5,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,4,1,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,4,7,1,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,4,7,5,1] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,5,1,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,5,4,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,2,6,5,7,1,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,2,6,5,7,4,1] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,4,1,5,7,2,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,4,1,5,7,6,2] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,4,1,6,2,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,4,1,6,5,7,2] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => 1

[3,4,1,6,7,5,2] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => 1

[3,4,2,5,7,1,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,4,2,5,7,6,1] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,4,2,6,1,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,4,2,6,5,7,1] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,4,2,6,7,1,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => 1

[3,4,2,6,7,5,1] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,2,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,1,2,7,6,4] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,1,4,7,2,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,1,4,7,6,2] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,1,6,2,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,6,4,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,6,2,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,1,7,6,4,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,1,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,2,1,7,6,4] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,2,4,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,2,4,7,6,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,2,6,1,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,6,4,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,1,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,1,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,4,1,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,4,6,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,6,1,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,2,7,6,4,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,1,7,2,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,4,1,7,6,2] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,4,2,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,4,2,7,6,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[3,5,4,6,1,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,6,2,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,1,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,1,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,2,1,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,2,6,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,6,1,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,4,7,6,2,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => 1

[3,5,6,1,7,2,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,5,6,1,7,4,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,5,6,2,7,1,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,5,6,2,7,4,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,5,6,4,7,1,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[3,5,6,4,7,2,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,1,2,5,7,6,3] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,2,6,5,7,3] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,7,3,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,7,5,3,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,7,5,6,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,2,7,6,5,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,1,3,5,7,6,2] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,1,3,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,3,6,5,7,2] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,3,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,7,2,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,7,5,2,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,7,5,6,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,3,7,6,5,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,1,5,2,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,5,2,7,6,3] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,5,3,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,5,3,7,6,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,1,5,7,2,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,5,7,2,6,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,5,7,3,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,5,7,3,6,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,5,7,6,2,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,5,7,6,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,2,7,5,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,3,7,5,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,2,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,2,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,3,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,3,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,7,2,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,1,6,5,7,3,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,1,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,2,1,5,7,6,3] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,2,1,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,1,6,5,7,3] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,1,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,1,7,3,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,1,7,5,3,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,1,7,5,6,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,1,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,1,7,6,5,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,2,3,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,2,3,6,1,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,3,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,3,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,7,1,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,7,5,1,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,7,6,1,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,3,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,2,5,1,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,5,1,7,6,3] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,5,3,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,5,3,7,6,1] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,2,5,7,1,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,5,7,1,6,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,5,7,3,1,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,5,7,3,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,5,7,6,1,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,5,7,6,3,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,1,7,5,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,3,7,5,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,1,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,1,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,3,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,3,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,7,1,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,2,6,5,7,3,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,1,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,3,1,5,7,6,2] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,3,1,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,1,6,5,7,2] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,1,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,1,7,2,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,1,7,5,2,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,1,7,5,6,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,1,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,1,7,6,5,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,3,2,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => ([(0,2),(2,1)],3) => 1

[4,3,2,6,1,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,2,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,2,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,7,1,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,7,5,1,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,7,6,1,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,2,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => ([(0,2),(2,1)],3) => 1

[4,3,5,1,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,5,1,7,6,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,5,2,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,5,2,7,6,1] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[4,3,5,7,1,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,5,7,1,6,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,5,7,2,1,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,5,7,2,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,5,7,6,1,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,5,7,6,2,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,1,7,5,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,2,7,5,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,1,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,1,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,2,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,2,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,7,1,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[4,3,6,5,7,2,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => 1

[2,3,4,1,6,7,8,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 2

[1,3,4,5,2,7,8,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,2,4,5,3,7,8,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,1,3,5,4,7,8,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,2],[2,1,1]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 2

[2,3,4,1,5,7,8,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 1

[1,3,4,2,5,7,8,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2

[2,3,1,4,5,7,8,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 1

[2,1,4,5,6,3,8,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2

[1,2,3,5,6,4,8,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,4,1,6,5,8,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2

[2,1,3,4,6,5,8,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,2],[2,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2

[1,2,3,4,6,5,8,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 1

[1,3,4,5,2,6,8,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

[1,2,3,5,4,6,8,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[1,3,4,2,5,6,8,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

[2,1,4,3,5,6,8,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,2],[2,2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2

[1,2,4,3,5,6,8,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,3,2,4,5,6,8,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,5,6,7,4,8] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[2,3,4,1,6,7,5,8] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[1,2,4,3,6,7,5,8] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1,1],[3,1]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 2

[2,3,1,4,6,7,5,8] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[5,5,3,3],[4,2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2

[2,1,3,4,6,7,5,8] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,2],[3,1,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2

[1,3,4,5,2,7,6,8] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2

[1,2,3,5,4,7,6,8] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2

[2,3,4,1,5,7,6,8] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,4,5,7,6,8] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,3,2,4,5,7,6,8] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2

[2,1,3,4,5,7,6,8] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,5,6,4,7,8] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[2,3,4,1,6,5,7,8] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 1

[2,1,3,4,6,5,7,8] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,2,3,4,6,5,7,8] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 1

[2,1,4,5,3,6,7,8] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[2,3,1,5,4,6,7,8] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 1

[1,3,2,5,4,6,7,8] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2

[2,1,3,5,4,6,7,8] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[1,2,3,5,4,6,7,8] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 2

[2,1,4,3,5,6,7,8] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 1

[1,2,4,3,5,6,7,8] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 1

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Description

The global dimension of the incidence algebra of the lattice over the rational numbers.

Map

skew partition

Description

The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let

$D$ be a Dyck path of semilength

$n$ . The parallelogram polyomino

$\gamma(D)$ is defined as follows: let

$\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to

$D$ . Then, the upper path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with even indices, and the lower path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of

$\gamma(D)$ .

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.

Map

dominating sublattice

Description

Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function

$s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions

$\nu$ with

$c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example

$\lambda = (5^2,4^2,1)$ and

$\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.