Identifier
Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[1,0] => [1,1,0,0] => [1,2] => ([(0,1)],2)
[1,0,1,0] => [1,1,0,1,0,0] => [2,1,3] => ([(0,2),(1,2)],3)
[1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => ([(0,2),(2,1)],3)
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
>>> Load all 655 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => ([(0,7),(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,7),(6,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => ([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => ([(0,7),(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => ([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => ([(0,7),(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => ([(0,7),(1,7),(2,5),(3,4),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,7),(6,5)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => ([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => ([(0,7),(1,7),(2,6),(3,4),(4,6),(5,7),(6,5)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,7),(6,5)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => ([(0,7),(1,7),(2,4),(3,5),(4,7),(5,6),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => ([(0,5),(1,4),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => ([(0,7),(1,7),(2,4),(3,5),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => ([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => ([(0,7),(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => ([(0,7),(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => ([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => ([(0,7),(1,5),(2,6),(3,7),(5,7),(6,3),(7,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,5),(7,4)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => ([(0,6),(1,5),(2,4),(4,7),(5,7),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,5),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(6,7),(7,5)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => ([(0,6),(1,6),(2,5),(3,5),(5,7),(6,7),(7,4)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => ([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,5),(7,6)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => ([(0,7),(1,7),(2,6),(3,4),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => ([(0,7),(1,5),(2,4),(4,7),(5,7),(6,3),(7,6)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => ([(0,7),(1,5),(2,4),(4,7),(5,7),(6,3),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => ([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,7,5,6,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8,6,5,7,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,7,5,8,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8,5,6,7,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,8),(7,6)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,8),(7,6)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,7)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,2,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(8,6)],9)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => ([(0,8),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,6)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => ([(0,8),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,1,9] => ([(0,7),(1,8),(2,4),(3,7),(4,8),(5,3),(6,5),(8,6)],9)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => ([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,3,4,5,6,8,1,2,9] => ([(0,7),(1,6),(2,4),(3,7),(4,8),(5,3),(6,5),(7,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,8),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(8,7)],9)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(8,7)],9)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(7,6),(8,7)],9)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,7,1,8,9] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,8),(7,6),(8,7)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => ([(0,8),(1,8),(2,7),(3,8),(5,6),(6,3),(7,5),(8,4)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(7,6),(8,7)],9)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(7,8),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [6,7,4,3,2,1,5,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(7,6),(8,7)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,8),(6,7),(8,6)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(7,5),(8,7)],9)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => ([(0,7),(1,8),(2,6),(3,6),(4,5),(6,7),(7,8),(8,4)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => ([(0,8),(1,8),(2,6),(4,8),(5,4),(6,5),(7,3),(8,7)],9)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => ([(0,7),(1,8),(2,8),(3,6),(4,5),(5,7),(6,8),(7,6)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,1,2,6,8,9] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,8),(7,6),(8,7)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,8),(6,7),(8,6)],9)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => ([(0,6),(1,5),(2,4),(4,8),(5,8),(6,8),(7,3),(8,7)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(7,6),(8,5)],9)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,6),(6,7),(8,5)],9)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => ([(0,8),(1,8),(2,6),(4,8),(5,3),(6,4),(7,5),(8,7)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,7),(4,6),(6,5),(7,4),(8,7)],9)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => ([(0,8),(1,7),(2,4),(4,7),(5,3),(6,5),(7,8),(8,6)],9)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => ([(0,8),(1,8),(2,6),(4,8),(5,3),(6,4),(7,5),(8,7)],9)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => ([(0,7),(1,6),(3,8),(4,8),(5,2),(6,3),(7,4),(8,5)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => ([(0,7),(1,8),(2,6),(3,5),(5,8),(6,7),(7,4),(8,6)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,6),(6,7),(8,5)],9)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => ([(0,8),(1,8),(2,4),(4,7),(5,3),(6,5),(7,6),(8,7)],9)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => ([(0,7),(1,4),(3,8),(4,8),(5,2),(6,5),(7,3),(8,6)],9)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,1,3,6,7,8,9] => ([(0,8),(1,8),(2,4),(4,7),(5,3),(6,5),(7,6),(8,7)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => ([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => ([(0,7),(1,8),(2,4),(3,7),(4,8),(5,3),(6,5),(8,6)],9)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => ([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => ([(0,8),(1,7),(2,7),(4,6),(5,4),(6,3),(7,8),(8,5)],9)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => ([(0,7),(1,8),(2,4),(3,7),(4,8),(5,3),(6,5),(8,6)],9)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => ([(0,8),(1,7),(2,4),(4,7),(5,3),(6,5),(7,8),(8,6)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => ([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => ([(0,4),(1,3),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => ([(0,8),(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => ([(0,9),(1,9),(2,8),(3,8),(4,5),(5,7),(6,4),(7,3),(9,6)],10)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => ([(0,9),(1,9),(2,8),(3,9),(4,5),(5,7),(6,4),(7,3),(8,6)],10)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => ([(0,9),(1,3),(2,10),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],11)
[] => [1,0] => [1] => ([],1)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(9,8)],10)
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => ([(0,6),(1,6),(2,9),(3,7),(4,8),(6,8),(7,9),(8,7),(9,5)],10)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => ([(0,8),(1,7),(2,6),(3,5),(5,9),(6,9),(7,9),(8,9),(9,4)],10)
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => ([(0,8),(1,4),(2,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,3)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,9),(7,8),(9,7)],10)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,9),(7,8),(9,7)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,7),(7,8),(9,6)],10)
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => ([(0,8),(1,7),(2,9),(3,9),(5,2),(6,3),(7,5),(8,6),(9,4)],10)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,7),(7,8),(9,6)],10)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(7,6),(8,7),(9,5)],10)
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9,10] => ([(0,9),(1,9),(2,7),(4,9),(5,6),(6,3),(7,4),(8,5),(9,8)],10)
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => ([(0,9),(1,8),(2,4),(4,8),(5,7),(6,5),(7,3),(8,9),(9,6)],10)
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => ([(0,8),(1,7),(3,9),(4,9),(5,2),(6,5),(7,3),(8,4),(9,6)],10)
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(3,9),(5,7),(6,5),(7,4),(8,6),(9,8)],10)
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => ([(0,9),(1,9),(2,4),(4,9),(5,7),(6,5),(7,3),(8,6),(9,8)],10)
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => ([(0,9),(1,8),(2,8),(4,5),(5,7),(6,4),(7,3),(8,9),(9,6)],10)
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => ([(0,9),(1,9),(2,4),(4,9),(5,7),(6,5),(7,3),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => ([(0,4),(1,3),(3,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => ([(0,9),(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,6,9,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,9,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(9,8)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(9,8)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,8,10,7,6,5,4,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,7,10,6,5,4,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(9,10)],11)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,10,4,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,9),(5,9),(6,9),(7,9),(8,9),(9,10)],11)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,10,3,2,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(10,9)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,10,1,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(10,9)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(10,9)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7,6,8,9,5,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,9),(8,7)],10)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,9),(8,7)],10)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,8,9,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,8),(6,8),(7,9),(8,7)],10)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,8,9,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(9,7)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => ([(0,8),(1,7),(2,6),(3,9),(4,9),(5,9),(6,3),(7,4),(8,5)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => ([(0,5),(1,9),(2,9),(3,9),(4,9),(5,8),(6,9),(7,6),(8,7)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5,11] => ([(0,9),(1,8),(2,10),(3,10),(4,6),(5,7),(6,2),(7,3),(8,4),(9,5)],11)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(9,8)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(9,8)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,8)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,10),(7,8),(8,9),(10,7)],11)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10,11] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,10),(7,8),(8,9),(10,7)],11)
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => ([(0,10),(1,3),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => ([(0,10),(1,3),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => ([(0,11),(1,3),(3,11),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8),(11,10)],12)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,5,2,1,10] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,2,3,1,4,6,8,10] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
searching the database
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