Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Images
[1,0] => [1] => ([],1) => [1]
[1,0,1,0] => [2,1] => ([(0,1)],2) => [2]
[1,1,0,0] => [1,2] => ([],2) => [1,1]
[1,0,1,0,1,0] => [2,1,3] => ([(1,2)],3) => [2,1]
[1,0,1,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => [3]
[1,1,0,0,1,0] => [3,1,2] => ([(0,2),(1,2)],3) => [3]
[1,1,0,1,0,0] => [1,3,2] => ([(1,2)],3) => [2,1]
[1,1,1,0,0,0] => [1,2,3] => ([],3) => [1,1,1]
[1,0,1,0,1,0,1,0] => [2,1,4,3] => ([(0,3),(1,2)],4) => [2,2]
[1,0,1,0,1,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => [4]
[1,0,1,1,0,0,1,0] => [2,1,3,4] => ([(2,3)],4) => [2,1,1]
[1,0,1,1,0,1,0,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => [3,1]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => [4]
[1,1,0,0,1,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => [4]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => [4]
[1,1,0,1,0,0,1,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => [3,1]
[1,1,0,1,0,1,0,0] => [1,3,2,4] => ([(2,3)],4) => [2,1,1]
[1,1,0,1,1,0,0,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => [3,1]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => [4]
[1,1,1,0,0,1,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => [3,1]
[1,1,1,0,1,0,0,0] => [1,2,4,3] => ([(2,3)],4) => [2,1,1]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => [1,1,1,1]
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => [2,2,1]
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => [4,1]
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => [3,2]
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => [5]
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [5]
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => [3,2]
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => [2,2,1]
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => [3,2]
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => ([(3,4)],5) => [2,1,1,1]
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => [3,1,1]
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => [4,1]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5]
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => [4,1]
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => [4,1]
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [5]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [5]
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => [5]
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [5]
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => [3,2]
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => [2,2,1]
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => [4,1]
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => [3,1,1]
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => ([(3,4)],5) => [2,1,1,1]
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => [3,1,1]
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => [4,1]
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [5]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [5]
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => [4,1]
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => [4,1]
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => [4,1]
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => [3,1,1]
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => ([(3,4)],5) => [2,1,1,1]
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => [3,1,1]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5]
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => [4,1]
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => [3,1,1]
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => ([(3,4)],5) => [2,1,1,1]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => [1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => [2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => [4,2]
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => [4,2]
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [6]
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => [5,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => [4,2]
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6) => [4,2]
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [6]
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,2]
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [6]
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3]
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => [4,2]
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3]
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [6]
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => [4,2]
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
>>> Load all 846 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => ([(4,5)],6) => [2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => [4,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,1]
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [6]
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => [6]
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => [5,1]
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => [5,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => ([(4,5)],6) => [2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [6]
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,1]
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [6]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => [5,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => [4,2]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => [3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => [2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => ([(4,5)],6) => [2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [6]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => [5,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => [4,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => ([(4,5)],6) => [2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => [4,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => [3,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => ([(4,5)],6) => [2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([],6) => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => [2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [6,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [5,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7) => [2,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [5,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [7]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [5,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [7]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => [2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [7]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [7]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [6,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [7]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [5,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => [2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [6,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [7]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [6,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [7]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [6,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [7]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [6,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => ([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => [2,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => ([(4,6),(5,6)],7) => [3,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => ([(5,6)],7) => [2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([],7) => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => ([(0,7),(1,6),(2,5),(3,4)],8) => [2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8) => [8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8) => [7,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => [8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [8]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => ([(0,7),(1,6),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => [4,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,7,8,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => [8]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => ([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => [4,2,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => ([(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(6,7)],8) => [8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8) => [8]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8) => [8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,7,4,8,6] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => [8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,7,4,8,5] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [6,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5,8] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => [7,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => ([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7)],8) => [8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => ([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,7,8,3,4,5,6] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => [4,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [3,4,6,1,2,7,8,5] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7)],8) => [8]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => [4,4]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6),(6,7)],8) => [8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8) => [8]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => [8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => ([(0,4),(0,5),(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8) => [7,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,7,8,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8) => [7,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => [8]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,5,1,2,4,8,6,7] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => ([(0,4),(0,5),(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [8]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,8,4,5,7] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => ([(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(6,7)],8) => [8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => [8]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,8,4,5,7] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8) => [8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,7,4,8,5,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => [7,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [6,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [6,1,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => [8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => ([(0,4),(0,5),(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [8]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,8,6,7] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => ([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [6,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6),(6,7)],8) => [8]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => ([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => [7,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => [7,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => ([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => ([(0,7),(1,6),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => [8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8) => [7,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8) => [8]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => [8]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [6,1,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => ([(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(6,7)],8) => [8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8) => [8]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8) => [7,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => ([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => [7,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [8]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [7,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => [6,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => ([(4,7),(5,6)],8) => [2,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [7,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => [6,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => ([],8) => [1,1,1,1,1,1,1,1]
[] => [] => ([],0) => []
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,9,6] => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9) => [6,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => [9]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8,9] => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9) => [6,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9) => [6,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => [9]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,7] => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9) => [9]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
searching the database
Sorry, this map was not found in the database.