Identifier
Values
[1,0] => ([],1) => [1] => [1] => 1
[1,0,1,0] => ([(0,1)],2) => [2] => [1,1] => 2
[1,1,0,0] => ([(0,1)],2) => [2] => [1,1] => 2
[1,0,1,0,1,0] => ([(0,2),(2,1)],3) => [3] => [1,1,1] => 3
[1,0,1,1,0,0] => ([(0,2),(2,1)],3) => [3] => [1,1,1] => 3
[1,1,0,0,1,0] => ([(0,2),(2,1)],3) => [3] => [1,1,1] => 3
[1,1,0,1,0,0] => ([(0,2),(2,1)],3) => [3] => [1,1,1] => 3
[1,1,1,0,0,0] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => [2,1,1] => 4
[1,0,1,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,0,1,0,1,1,0,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,0,1,1,0,0,1,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,0,1,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,0,1,1,1,0,0,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => [2,1,1,1] => 5
[1,1,0,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,1,0,0,1,1,0,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,1,0,1,0,0,1,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,1,0,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,1,1,1] => 4
[1,1,0,1,1,0,0,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => [2,1,1,1] => 5
[1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => [2,1,1,1] => 5
[1,1,1,0,0,1,0,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => [2,1,1,1] => 5
[1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => [2,2,1,1] => 6
[1,1,1,1,0,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => [2,2,1,1] => 6
[1,0,1,0,1,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => [2,1,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,1,0,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => [2,1,1,1,1] => 6
[1,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => [2,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => [2,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => [2,2,1,1,1] => 7
[1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,0,1,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,0,1,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,1,0,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,1,1,1,1] => 5
[1,1,0,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,0,1,1,1,0,0,0,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,0,0,0,1,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,1,0,0,1,0,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,1,0,0,1,0,1,0,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => [2,1,1,1,1] => 6
[1,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,0,1,0,0,0,1,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,0,1,0,0,1,0,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,0,1,0,1,0,0,0] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => [5,3] => [2,2,2,1,1] => 8
[1,1,1,0,1,1,0,0,0,0] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => [5,3] => [2,2,2,1,1] => 8
[1,1,1,1,0,0,0,0,1,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,1,0,0,0,1,0,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => [2,2,1,1,1] => 7
[1,1,1,1,0,0,1,0,0,0] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => [5,3] => [2,2,2,1,1] => 8
[1,1,1,1,0,1,0,0,0,0] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => [5,3] => [2,2,2,1,1] => 8
[1,1,1,1,1,0,0,0,0,0] => ([(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) => [5,3,1] => [3,2,2,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
>>> Load all 523 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => [6,3,1] => [3,2,2,1,1,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,0,1,1,1,1,0,0,0,0,0] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => [6,3,1] => [3,2,2,1,1,1] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => [2,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,0,1,0,1,1,0,0,0,0] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => [6,4,1] => [3,2,2,2,1,1] => 11
[1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => [2,2,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => [6,3] => [2,2,2,1,1,1] => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => [6,4] => [2,2,2,2,1,1] => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => [6,4,1] => [3,2,2,2,1,1] => 11
[1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => [6,3,1] => [3,2,2,1,1,1] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => [6,3,1] => [3,2,2,1,1,1] => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11) => [6,4,1] => [3,2,2,2,1,1] => 11
[1,1,1,1,1,0,0,1,0,0,0,0] => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11) => [6,4,1] => [3,2,2,2,1,1] => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => [6,4,2] => [3,3,2,2,1,1] => 12
[1,1,1,1,1,1,0,0,0,0,0,0] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => [6,4,2] => [3,3,2,2,1,1] => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => [7,4,1] => [3,2,2,2,1,1,1] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => [7,4,1] => [3,2,2,2,1,1,1] => 12
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => [2,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => [7,4,1] => [3,2,2,2,1,1,1] => 12
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => [2,2,2,1,1,1,1] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11) => [7,4] => [2,2,2,2,1,1,1] => 11
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => [7,4,1] => [3,2,2,2,1,1,1] => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => [7,5] => [2,2,2,2,2,1,1] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => [7,5] => [2,2,2,2,2,1,1] => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [8,3] => [2,2,2,1,1,1,1,1] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => [10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => [9] => [1,1,1,1,1,1,1,1,1] => 9
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Description
The number of different non-empty partial sums of an integer partition.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
Greene-Kleitman invariant
Description
The Greene-Kleitman invariant of a poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.
Map
parallelogram poset
Description
The cell poset of the parallelogram polyomino corresponding to the Dyck path.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the cell poset of $\gamma(D)$. In this partial order, the cells of the polyomino are the elements and a cell covers those cells with which it shares an edge and which are closer to the origin.