- FindStat

Identifier

Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000189: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 823 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[7,1],[1]] => [1] => [[1],[]] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,4],[1]] => [1] => [[1],[]] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6,4],[1]] => [1] => [[1],[]] => ([],1) => 1

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

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

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

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

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

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

[[6,5],[1]] => [1] => [[1],[]] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,4,4],[1]] => [1] => [[1],[]] => ([],1) => 1

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

[[5,5,4],[1]] => [1] => [[1],[]] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,5,5,5],[4,1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5

[[3,3,3,3,3,3],[2]] => [2] => [[2],[]] => ([(0,1)],2) => 2

[[4,4,4,4,3],[3]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3

[[5,5,5,4],[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[[4,4,4,4,4],[3,1]] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4

[[5,5,5,5],[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[[4,4,4,4,4],[3]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3

[[8,8],[6]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[5,5,5,5,5],[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[[5,5,5,5,5,5],[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[[4,4,4,4,4,4],[3]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3

[[6,6,6,6,6,6],[5]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[[6,6,6,6,6],[5]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[[5,5,5,5,4],[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[[5,5,5,5,5],[4,1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5

[[5,5,5,5,1],[1]] => [1] => [[1],[]] => ([],1) => 1

search for individual values

searching the database for the individual values of this statistic

Description

The number of elements in the poset.

Map

to skew partition

Description

The partition regarded as a skew partition.

Map

cell poset

Description

The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.

Map

inner shape

Description

The inner shape of a skew partition.