- FindStat

Identifier

Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000772: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 580 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1]] => [[1]] => [1] => ([],1) => 1

[[2]] => [[2]] => [1] => ([],1) => 1

[[3]] => [[3]] => [1] => ([],1) => 1

[[4]] => [[4]] => [1] => ([],1) => 1

[[5]] => [[5]] => [1] => ([],1) => 1

[[6]] => [[6]] => [1] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The multiplicity of the largest distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).

Map

catabolism

Description

Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).

Map

graph of inversions

Description

The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.