Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000070: Posets ⟶ ℤ
Values
[1,1] => [1] => [[1],[]] => ([],1) => 2
[2,1] => [1] => [[1],[]] => ([],1) => 2
[1,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[3,1] => [1] => [[1],[]] => ([],1) => 2
[2,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[2,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[1,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[4,1] => [1] => [[1],[]] => ([],1) => 2
[3,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[3,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[2,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[2,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[1,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[5,1] => [1] => [[1],[]] => ([],1) => 2
[4,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[4,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[3,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[3,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[3,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[2,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[2,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[2,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[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) => 6
[6,1] => [1] => [[1],[]] => ([],1) => 2
[5,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[5,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[4,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[4,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[4,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[3,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[3,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[3,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[3,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[2,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[2,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[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) => 6
[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) => 7
[7,1] => [1] => [[1],[]] => ([],1) => 2
[6,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[6,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[5,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[5,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[5,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[4,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[4,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[4,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[4,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[4,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[3,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[3,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[3,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[3,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[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) => 10
[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) => 12
[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) => 11
[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) => 7
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[8,1] => [1] => [[1],[]] => ([],1) => 2
[7,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[7,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[6,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[6,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[6,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[5,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[5,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[5,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[5,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[5,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[4,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[4,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[4,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[4,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[4,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[3,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[3,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[3,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[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) => 10
[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) => 12
[3,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[2,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[2,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[9,1] => [1] => [[1],[]] => ([],1) => 2
[8,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[8,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[7,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[7,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[7,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[6,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[6,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[6,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[6,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[6,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[5,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[5,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[5,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
>>> Load all 700 entries. <<<[5,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[5,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[5,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[4,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[4,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[4,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[4,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[4,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[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) => 10
[4,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[4,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[3,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[3,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[3,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[3,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[3,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[3,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[2,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[2,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[10,1] => [1] => [[1],[]] => ([],1) => 2
[9,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[9,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[8,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[8,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[8,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[7,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[7,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[7,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[7,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[7,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[6,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[6,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[6,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[6,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[6,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[6,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[5,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[5,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[5,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[5,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[5,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[5,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[5,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[5,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[5,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[4,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[4,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[4,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[4,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[4,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[4,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[4,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[4,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[4,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[3,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[3,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[3,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[3,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[3,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[3,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[2,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[11,1] => [1] => [[1],[]] => ([],1) => 2
[10,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[10,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[9,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[9,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[9,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[8,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[8,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[8,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[8,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[8,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[7,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[7,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[7,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[7,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[7,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[7,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[6,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[6,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[6,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[6,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[6,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[6,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[6,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[6,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[6,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[6,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[5,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[5,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[5,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[5,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[5,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[5,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[5,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[5,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[5,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[5,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[5,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[4,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[4,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[4,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[4,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[4,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[4,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[4,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[4,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[4,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[4,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[4,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[3,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[3,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[3,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[3,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[3,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[3,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[12,1] => [1] => [[1],[]] => ([],1) => 2
[11,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[11,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[10,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[10,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[10,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[9,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[9,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[9,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[9,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[9,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[8,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[8,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[8,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[8,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[8,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[8,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[7,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[7,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[7,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[7,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[7,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[7,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[7,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[7,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[7,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[7,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[6,6,1] => [6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[6,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[6,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[6,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[6,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[6,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[6,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[6,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[6,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[6,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[6,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[6,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[5,5,3] => [5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[5,5,2,1] => [5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[5,5,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[5,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[5,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[5,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[5,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[5,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[5,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[5,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[5,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[5,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[5,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[5,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[4,4,4,1] => [4,4,1] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[4,4,3,2] => [4,3,2] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[4,4,3,1,1] => [4,3,1,1] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[4,4,2,2,1] => [4,2,2,1] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[4,4,2,1,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[4,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[4,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[4,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[4,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[4,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[4,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[13,1] => [1] => [[1],[]] => ([],1) => 2
[12,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[12,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[11,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[11,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[11,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[10,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[10,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[10,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[10,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[10,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[9,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[9,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[9,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[9,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[9,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[9,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[8,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[8,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[8,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[8,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[8,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[8,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[8,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[8,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[8,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[8,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[7,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[7,6,1] => [6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[7,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[7,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[7,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[7,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[7,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[7,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[7,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[7,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[7,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[7,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[7,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[6,6,2] => [6,2] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[6,6,1,1] => [6,1,1] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[6,5,3] => [5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[6,5,2,1] => [5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[6,5,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[6,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[6,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[6,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[6,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[6,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[6,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[6,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[6,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[6,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[6,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[6,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[5,5,4] => [5,4] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[5,5,3,1] => [5,3,1] => [[5,3,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[5,5,2,2] => [5,2,2] => [[5,2,2],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[5,5,2,1,1] => [5,2,1,1] => [[5,2,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[5,5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => 26
[5,4,4,1] => [4,4,1] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[5,4,3,2] => [4,3,2] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[5,4,3,1,1] => [4,3,1,1] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[5,4,2,2,1] => [4,2,2,1] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[5,4,2,1,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[5,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[5,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[5,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[5,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[5,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[5,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[14,1] => [1] => [[1],[]] => ([],1) => 2
[13,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[13,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[12,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[12,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[12,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[11,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[11,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[11,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[11,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[11,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[10,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[10,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[10,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[10,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[10,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[10,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[9,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[9,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[9,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[9,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[9,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[9,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[9,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[9,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[9,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[9,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[8,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[8,6,1] => [6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[8,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[8,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[8,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[8,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[8,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[8,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[8,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[8,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[8,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[8,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[8,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[7,7,1] => [7,1] => [[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[7,6,2] => [6,2] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[7,6,1,1] => [6,1,1] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[7,5,3] => [5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[7,5,2,1] => [5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[7,5,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[7,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[7,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[7,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[7,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[7,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[7,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[7,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[7,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[7,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[7,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[7,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[6,6,3] => [6,3] => [[6,3],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[6,6,2,1] => [6,2,1] => [[6,2,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[6,6,1,1,1] => [6,1,1,1] => [[6,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[6,5,4] => [5,4] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[6,5,3,1] => [5,3,1] => [[5,3,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[6,5,2,2] => [5,2,2] => [[5,2,2],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[6,5,2,1,1] => [5,2,1,1] => [[5,2,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[6,5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => 26
[6,4,4,1] => [4,4,1] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[6,4,3,2] => [4,3,2] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[6,4,3,1,1] => [4,3,1,1] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[6,4,2,2,1] => [4,2,2,1] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[6,4,2,1,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[6,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[6,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[6,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[6,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[6,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[6,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[15,1] => [1] => [[1],[]] => ([],1) => 2
[14,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[14,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[13,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[13,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[13,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[12,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[12,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[12,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[12,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[12,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[11,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[11,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[11,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[11,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[11,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[11,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[10,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[10,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[10,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[10,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[10,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[10,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[10,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[10,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[10,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[10,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[9,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[9,6,1] => [6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[9,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[9,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[9,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[9,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[9,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[9,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[9,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[9,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[9,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[9,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[9,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[8,8] => [8] => [[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[8,7,1] => [7,1] => [[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[8,6,2] => [6,2] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[8,6,1,1] => [6,1,1] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[8,5,3] => [5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[8,5,2,1] => [5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[8,5,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[8,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[8,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[8,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[8,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[8,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[8,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[8,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[8,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[8,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[8,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[8,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[7,7,2] => [7,2] => [[7,2],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[7,7,1,1] => [7,1,1] => [[7,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[7,6,3] => [6,3] => [[6,3],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[7,6,2,1] => [6,2,1] => [[6,2,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[7,6,1,1,1] => [6,1,1,1] => [[6,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[7,5,4] => [5,4] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[7,5,3,1] => [5,3,1] => [[5,3,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[7,5,2,2] => [5,2,2] => [[5,2,2],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[7,5,2,1,1] => [5,2,1,1] => [[5,2,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[7,5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => 26
[7,4,4,1] => [4,4,1] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[7,4,3,2] => [4,3,2] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[7,4,3,1,1] => [4,3,1,1] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[7,4,2,2,1] => [4,2,2,1] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[7,4,2,1,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[7,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[7,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[7,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[7,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[7,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[7,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[16,1] => [1] => [[1],[]] => ([],1) => 2
[15,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[15,1,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[14,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[14,2,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[14,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[13,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[13,3,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[13,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[13,2,1,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 7
[13,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[12,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[12,4,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[12,3,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[12,3,1,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 10
[12,2,2,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 9
[12,2,1,1,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 9
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[11,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[11,5,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[11,4,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[11,4,1,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[11,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[11,3,2,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 14
[11,3,1,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 13
[11,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
[11,2,2,1,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 12
[11,2,1,1,1,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 11
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[10,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[10,6,1] => [6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[10,5,2] => [5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[10,5,1,1] => [5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[10,4,3] => [4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[10,4,2,1] => [4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[10,4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 17
[10,3,3,1] => [3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[10,3,2,2] => [3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 16
[10,3,2,1,1] => [3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 19
[10,3,1,1,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 16
[10,2,2,2,1] => [2,2,2,1] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 14
[10,2,2,1,1,1] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 15
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 13
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8
[9,8] => [8] => [[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[9,7,1] => [7,1] => [[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[9,6,2] => [6,2] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[9,6,1,1] => [6,1,1] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[9,5,3] => [5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[9,5,2,1] => [5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[9,5,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[9,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[9,4,3,1] => [4,3,1] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[9,4,2,2] => [4,2,2] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[9,4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => 26
[9,4,1,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 21
[9,3,3,2] => [3,3,2] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 19
[9,3,3,1,1] => [3,3,1,1] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 22
[9,3,2,2,1] => [3,2,2,1] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 23
[9,3,2,1,1,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => 24
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 19
[9,2,2,2,2] => [2,2,2,2] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[9,2,2,2,1,1] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 18
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 18
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 15
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 9
[8,8,1] => [8,1] => [[8,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[8,7,2] => [7,2] => [[7,2],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[8,7,1,1] => [7,1,1] => [[7,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[8,6,3] => [6,3] => [[6,3],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[8,6,2,1] => [6,2,1] => [[6,2,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[8,6,1,1,1] => [6,1,1,1] => [[6,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[8,5,4] => [5,4] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[8,5,3,1] => [5,3,1] => [[5,3,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[8,5,2,2] => [5,2,2] => [[5,2,2],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[8,5,2,1,1] => [5,2,1,1] => [[5,2,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[8,5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => 26
[8,4,4,1] => [4,4,1] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[8,4,3,2] => [4,3,2] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[8,4,3,1,1] => [4,3,1,1] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[8,4,2,2,1] => [4,2,2,1] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => 32
[8,4,2,1,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => 33
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => 25
[8,3,3,3] => [3,3,3] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 20
[8,3,3,2,1] => [3,3,2,1] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 28
[8,3,3,1,1,1] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => 28
[8,3,2,2,2] => [3,2,2,2] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 25
[8,3,2,2,1,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => 30
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => 29
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 22
[8,2,2,2,2,1] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 20
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => 21
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 17
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
[10,4,4] => [4,4] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 15
[9,6,3] => [6,3] => [[6,3],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => 22
[9,9] => [9] => [[9],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 10
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Description
The number of antichains in a poset.
An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable.
An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in a poset.
An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable.
An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in a poset.
Map
first row removal
Description
Removes the first entry of an integer partition
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.
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.
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