- FindStat

Identifier

Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1196 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => ([(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] => [7,1,2,3,4,5,8,6] => ([(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] => [6,1,2,3,4,8,5,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => ([(0,7),(1,7),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6)],8)

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => ([(0,6),(1,6),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7)],8)

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => ([(0,7),(1,7),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => ([(0,7),(1,7),(2,3),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => ([(0,7),(1,4),(2,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => ([(0,4),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => ([(0,7),(1,7),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6)],8)

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => ([(0,7),(1,7),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => ([(0,5),(1,5),(2,3),(2,4),(2,6),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => ([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => ([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => ([(0,5),(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => ([(0,6),(1,4),(2,4),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => ([(0,4),(1,2),(1,4),(2,7),(3,5),(3,6),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => ([(0,2),(1,2),(1,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => ([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => ([(0,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => ([(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => ([(0,7),(1,4),(2,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => ([(0,4),(1,7),(2,4),(2,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => ([(0,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => ([(0,7),(1,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => ([(0,6),(1,7),(2,3),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => ([(0,7),(1,3),(1,4),(2,5),(2,7),(3,4),(3,6),(4,6),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => ([(0,7),(1,6),(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] => [3,1,4,6,2,8,5,7] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => ([(0,6),(1,4),(2,5),(2,7),(3,5),(3,7),(4,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => ([(0,7),(1,7),(2,3),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => ([(0,3),(1,4),(2,6),(2,7),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => ([(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => ([(0,4),(1,2),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => ([(0,3),(1,2),(2,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => ([(0,2),(1,6),(1,7),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => ([(0,1),(1,5),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4] => ([(0,7),(1,7),(2,3),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => ([(0,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => ([(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => ([(0,7),(1,2),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => ([(0,6),(1,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => ([(0,6),(1,7),(2,3),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => ([(0,7),(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => ([(0,7),(1,4),(2,3),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => ([(0,7),(1,2),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => ([(0,2),(1,5),(1,7),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => ([(0,1),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => ([(0,7),(1,2),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => ([(0,7),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => ([(0,7),(1,7),(2,3),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => ([(0,7),(1,2),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => ([(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] => [2,7,1,3,4,5,8,6] => ([(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] => [2,6,1,3,4,8,5,7] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => ([(0,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => ([(0,7),(1,5),(2,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6] => ([(0,7),(1,3),(2,5),(2,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => ([(0,5),(1,2),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => ([(0,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8)

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => ([(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => ([(0,3),(1,4),(2,6),(2,7),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => ([(0,3),(1,5),(1,7),(2,4),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => ([(0,4),(1,7),(2,4),(2,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => ([(0,7),(1,3),(2,3),(2,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => ([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => ([(0,6),(1,2),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => ([(0,4),(1,7),(2,4),(2,7),(3,5),(3,6),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => ([(0,2),(1,2),(1,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => ([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => ([(0,6),(1,6),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7)],8)

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => ([(0,5),(1,2),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => ([(0,6),(1,4),(1,7),(2,4),(2,7),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7] => ([(0,6),(1,4),(2,5),(2,7),(3,5),(3,7),(4,6),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(6,7)],8)

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => ([(0,6),(1,6),(2,6),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => ([(0,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => ([(0,5),(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8)

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7)],8)

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => ([(0,4),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => ([(0,5),(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => ([(0,6),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => ([(0,7),(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6)],8)

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => ([(0,7),(1,3),(2,5),(2,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => ([(0,4),(1,2),(1,4),(2,7),(3,5),(3,6),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(6,7)],8)

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => ([(0,7),(1,7),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(5,6)],8)

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => ([(0,3),(1,5),(1,7),(2,4),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7)],8)

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => ([(0,5),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => ([(0,2),(1,6),(1,7),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => ([(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => ([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => ([(0,5),(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => ([(0,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => ([(0,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => ([(0,2),(1,5),(1,7),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => ([(0,6),(0,7),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => ([(0,4),(1,7),(2,4),(2,7),(3,5),(3,6),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => ([(0,7),(1,3),(1,4),(2,5),(2,7),(3,4),(3,6),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7)],8)

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => ([(0,6),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => ([(0,6),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => ([(0,7),(1,7),(2,3),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => ([(0,4),(1,4),(2,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => ([(0,7),(1,7),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(5,6)],8)

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => ([(0,7),(1,5),(2,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => ([(0,6),(1,4),(2,4),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => ([(0,6),(1,4),(1,7),(2,4),(2,7),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => ([(0,4),(1,4),(2,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => ([(0,7),(1,7),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => ([(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => ([(0,4),(1,2),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => ([(0,5),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => ([(0,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => ([(0,5),(1,5),(2,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => ([(0,7),(1,7),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6)],8)

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => ([(0,7),(1,3),(2,3),(2,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => ([(0,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => ([(0,6),(1,5),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => ([(0,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => ([(0,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => ([(0,6),(1,4),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => ([(0,7),(1,4),(2,3),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7)],8)

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => ([(0,5),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => ([(0,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,4),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => ([(0,2),(1,2),(1,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => ([(0,6),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => ([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => ([(0,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => ([(0,1),(1,5),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => ([(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => ([(0,6),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => ([(0,1),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => ([(0,3),(0,5),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => ([(0,5),(1,5),(2,3),(2,4),(2,6),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => ([(0,2),(1,2),(1,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => ([(0,5),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => ([(0,6),(0,7),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => ([(0,3),(0,5),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => ([(0,6),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => ([(0,6),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => ([(0,7),(1,2),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => ([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => ([(0,5),(1,5),(2,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => ([(0,7),(1,7),(2,3),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => ([(0,6),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => ([(0,7),(1,7),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => ([(0,6),(1,2),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => ([(0,7),(1,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => ([(0,6),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => ([(0,6),(1,4),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => ([(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => ([(0,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => ([(0,4),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => ([(0,7),(1,2),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => ([(0,6),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => ([(0,6),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => ([(0,4),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => ([(0,7),(1,7),(2,5),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => ([(0,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => ([(0,4),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => ([(0,5),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => ([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => ([(0,7),(1,7),(2,7),(3,4),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => ([(0,6),(1,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => ([(0,7),(1,7),(2,5),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => ([(0,7),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => ([(0,6),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => ([(0,6),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => ([(0,7),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => ([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => ([(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] => [8,1,2,3,4,5,6,9,7] => ([(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] => [7,1,2,3,4,5,9,6,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7)],9)

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)

[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)

[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,1,2,3,8,4,6,9,7] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => ([(0,8),(1,8),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,1,2,3,9,8,4,6,7] => ([(0,6),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7] => ([(0,8),(1,8),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,1,2,3,6,9,8,4,7] => ([(0,8),(1,7),(2,7),(3,7),(4,5),(4,6),(5,6),(5,8),(6,8),(7,8)],9)

[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)

[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)

[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [4,1,2,9,3,5,8,6,7] => ([(0,8),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,6),(5,8),(7,8)],9)

[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,9,3,8,5,6,7] => ([(0,6),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,8),(7,8)],9)

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => ([(0,8),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => ([(0,8),(1,8),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [4,1,2,8,9,3,5,6,7] => ([(0,6),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7] => ([(0,8),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [8,1,2,9,6,3,4,5,7] => ([(0,8),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,9,8,3,6,7] => ([(0,6),(1,5),(2,5),(3,7),(3,8),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [9,1,2,8,6,7,3,4,5] => ([(0,8),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,9,3,8] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)

[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,1,2,9,6,7,8,3,5] => ([(0,5),(1,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(6,8),(7,8)],9)

[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4] => ([(0,8),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)

[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,9,2,4,5,8,6,7] => ([(0,6),(1,8),(2,8),(3,6),(3,8),(4,7),(4,8),(5,7),(5,8),(7,8)],9)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,8] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)

[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,1,4,2,3,5,6,9,7] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [9,1,4,2,3,5,8,6,7] => ([(0,8),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,1,4,2,3,7,8,9,5] => ([(0,8),(1,7),(2,7),(3,7),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,1,7,2,3,4,5,9,6] => ([(0,8),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)

[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,4,9,2,5,8,6,7] => ([(0,8),(1,6),(2,5),(3,7),(3,8),(4,7),(4,8),(5,6),(6,8),(7,8)],9)

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,9,8,2,4,5,6,7] => ([(0,5),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [9,1,4,5,2,3,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [7,1,4,5,2,3,8,9,6] => ([(0,7),(1,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1,4,9,2,3,5,6,8] => ([(0,8),(1,7),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [9,1,6,5,2,3,4,7,8] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1,9,6,2,3,4,5,8] => ([(0,8),(1,7),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [9,1,8,6,2,3,4,5,7] => ([(0,8),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,4,8,9,2,5,6,7] => ([(0,8),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,8,9,7,2,4,5,6] => ([(0,1),(1,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [8,1,4,5,6,2,3,9,7] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8,1,4,9,7,2,3,5,6] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8,1,9,5,6,2,3,4,7] => ([(0,8),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,7,6,2,3,4,5] => ([(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,1,4,5,6,2,8,9,3] => ([(0,8),(1,7),(2,7),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,5,6,9,2,7,8] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)

[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,4,9,8,7,2,5,6] => ([(0,8),(1,2),(2,8),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,9,8,6,7,2,4,5] => ([(0,1),(1,6),(2,4),(2,5),(2,7),(2,8),(3,4),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [9,1,4,5,6,7,2,3,8] => ([(0,8),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [9,1,4,8,6,7,2,3,5] => ([(0,8),(1,5),(1,6),(1,8),(2,3),(2,4),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => ([(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3] => ([(0,8),(1,7),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,4,9,6,7,8,2,5] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,9,5,6,7,8,2,4] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,3] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,7,1,3,4,5,9,6,8] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)

[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,7,1,3,4,5,8,9,6] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,6,1,3,4,9,5,7,8] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)

[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,9,1,3,4,8,5,6,7] => ([(0,6),(1,8),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,8,1,3,9,4,5,6,7] => ([(0,6),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8)],9)

[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,9,1,3,8,7,4,5,6] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,9,1,3,6,7,8,4,5] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,9,1,8,3,4,5,6,7] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,7,1,6,3,4,8,9,5] => ([(0,6),(1,6),(2,5),(3,7),(3,8),(4,7),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,5,3,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,4),(4,7),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)

[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,8,9,3,5,6,7] => ([(0,5),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(6,7),(6,8)],9)

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,8,1,9,7,3,4,5,6] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,9,1,8,6,7,3,4,5] => ([(0,1),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)

[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,9,8,3,7] => ([(0,8),(1,8),(2,4),(3,6),(3,7),(4,5),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,9,1,5,6,7,8,3,4] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [9,3,1,2,4,5,8,6,7] => ([(0,8),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,3,1,2,4,7,8,9,5] => ([(0,8),(1,7),(2,7),(3,7),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [9,3,1,2,6,7,8,4,5] => ([(0,5),(0,8),(1,5),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,3,1,2,6,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(6,7),(7,8)],9)

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,4,1,2,3,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [7,4,1,2,3,5,8,9,6] => ([(0,8),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,4,1,2,3,7,8,9,5] => ([(0,6),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,9,1,2,3,4,6,7,8] => ([(0,8),(1,8),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,8,1,2,3,4,6,9,7] => ([(0,6),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8)],9)

[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,7,1,2,3,4,8,9,6] => ([(0,6),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8)],9)

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,6,1,2,3,4,5,7,8] => ([(0,8),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,6,1,2,3,4,5,9,7] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,7,1,2,3,4,5,9,6] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9,6,1,2,3,4,8,5,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,6,1,2,3,4,8,9,5] => ([(0,6),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,9,1,2,3,8,4,6,7] => ([(0,6),(0,8),(1,6),(1,8),(2,6),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,1,2,3,7,4,5,6] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8,6,1,2,3,7,4,9,5] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [9,6,1,2,3,7,8,4,5] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,1,2,3,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,4,1,2,9,3,6,7,8] => ([(0,6),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,4,1,2,9,3,5,6,7] => ([(0,6),(0,8),(1,6),(1,8),(2,6),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,8,1,2,9,3,4,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,6),(2,8),(3,6),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [9,7,1,2,6,3,8,4,5] => ([(0,7),(0,8),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9,8,1,2,6,7,3,4,5] => ([(0,7),(0,8),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [5,4,1,2,6,7,9,3,8] => ([(0,8),(1,8),(2,3),(3,8),(4,6),(4,7),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,4,1,2,6,7,8,9,3] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,3,1,9,2,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(5,8),(6,7)],9)

[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,1,8,2,4,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,4,1,8,2,3,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,9,1,5,2,3,4,7,8] => ([(0,8),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [9,7,1,6,2,3,4,5,8] => ([(0,8),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,1,9,2,3,4,5,6] => ([(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8,7,1,6,2,3,4,9,5] => ([(0,5),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [9,4,1,6,2,8,3,5,7] => ([(0,7),(0,8),(1,6),(1,8),(2,5),(2,6),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [9,8,1,6,2,7,3,4,5] => ([(0,7),(0,8),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,7,6,2,3,4,5] => ([(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [4,3,1,5,6,8,2,9,7] => ([(0,8),(1,8),(2,4),(3,6),(3,7),(4,5),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [4,3,1,5,9,8,2,6,7] => ([(0,8),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,3,1,5,8,7,2,9,6] => ([(0,7),(1,8),(2,5),(2,6),(3,4),(3,7),(3,8),(4,7),(4,8),(5,6),(5,8),(6,8)],9)

[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,9,1,5,6,7,2,3,4] => ([(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1,5,6,7,9,2,8] => ([(0,8),(1,8),(2,8),(3,4),(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1,5,6,9,8,2,7] => ([(0,8),(1,8),(2,6),(2,7),(3,4),(3,5),(4,5),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [9,3,1,5,6,7,8,2,4] => ([(0,5),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,4,1,5,6,7,8,2,3] => ([(0,5),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,2] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,8,1,4,5,6,9,7] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,9,1,4,5,8,6,7] => ([(0,8),(1,8),(2,6),(3,6),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,9,1,4,7,8,5,6] => ([(0,7),(1,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,9,1,8,7,4,5,6] => ([(0,5),(1,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,8,1,6,7,4,9,5] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)

[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,9,1,6,7,8,4,5] => ([(0,5),(1,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,9,4,1,3,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [2,6,4,1,3,7,8,9,5] => ([(0,7),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [2,9,5,1,3,4,6,7,8] => ([(0,8),(1,8),(2,8),(3,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,6,9,1,3,4,5,7,8] => ([(0,8),(1,8),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,9,7,1,3,4,5,6,8] => ([(0,8),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,8,1,3,4,5,6,7] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [2,6,7,1,3,4,8,9,5] => ([(0,6),(1,6),(2,5),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,9,4,1,6,3,5,7,8] => ([(0,7),(1,8),(2,8),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [2,8,4,1,9,3,5,6,7] => ([(0,6),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,8)],9)

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,9,4,1,6,3,8,5,7] => ([(0,7),(1,6),(1,8),(2,3),(2,4),(2,8),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [2,9,8,1,7,3,4,5,6] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [2,9,5,1,6,7,8,3,4] => ([(0,4),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,3,4,1,2,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [6,3,4,1,2,7,8,9,5] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,3,7,1,2,4,5,6,8] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,3,8,1,2,4,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,5,4,1,2,3,6,7,8] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [8,5,4,1,2,3,6,9,7] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,9,4,1,2,3,5,7,8] => ([(0,8),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,8,4,1,2,3,5,9,7] => ([(0,2),(1,7),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [9,7,4,1,2,3,5,6,8] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,4,1,2,3,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,9,5,1,2,3,4,7,8] => ([(0,8),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,8,5,1,2,3,4,9,7] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,7,5,1,2,3,4,9,6] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [6,7,9,1,2,3,4,5,8] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,9,8,1,2,3,4,5,7] => ([(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,5,4,1,2,8,3,9,7] => ([(0,2),(1,2),(1,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [9,8,5,1,7,2,3,4,6] => ([(0,6),(0,7),(0,8),(1,5),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,1,6,2,3,4,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [7,8,5,1,6,2,3,9,4] => ([(0,5),(1,6),(1,7),(1,8),(2,4),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [5,3,4,1,6,8,2,9,7] => ([(0,3),(1,8),(2,3),(2,8),(4,5),(4,6),(4,7),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [9,3,4,1,8,7,2,5,6] => ([(0,1),(0,2),(0,8),(1,5),(1,8),(2,5),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,3,4,1,6,7,2,9,5] => ([(0,6),(1,2),(1,3),(1,8),(2,7),(2,8),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9,5,4,1,8,7,2,3,6] => ([(0,6),(0,7),(0,8),(1,4),(1,5),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,5,4,1,6,7,2,9,3] => ([(0,7),(1,4),(1,7),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,3,4,1,9,7,8,2,6] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,6),(2,8),(3,6),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9,3,5,1,6,7,8,2,4] => ([(0,4),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9,5,4,1,6,7,8,2,3] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,2] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)

[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [2,3,4,9,1,5,8,6,7] => ([(0,8),(1,7),(2,7),(3,7),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,9,1,7,8,5,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)

[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,9,5,1,4,6,7,8] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [2,3,9,6,1,4,5,7,8] => ([(0,8),(1,8),(2,6),(3,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [2,3,7,9,1,4,5,6,8] => ([(0,8),(1,6),(2,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,9,8,1,4,5,6,7] => ([(0,6),(1,6),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [2,3,9,5,1,7,4,6,8] => ([(0,8),(1,7),(2,7),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,9,6,1,7,8,4,5] => ([(0,7),(1,7),(2,5),(2,6),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [2,9,4,5,1,3,6,7,8] => ([(0,8),(1,8),(2,8),(3,7),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [2,7,4,5,1,3,8,9,6] => ([(0,6),(1,6),(2,7),(3,4),(3,5),(3,8),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [2,9,8,6,1,3,4,5,7] => ([(0,5),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,7,8,9,1,3,4,5,6] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [2,8,9,6,1,7,3,4,5] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [2,9,6,5,1,7,8,3,4] => ([(0,3),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [7,3,4,5,1,2,8,9,6] => ([(0,5),(1,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9,3,4,8,1,2,5,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [7,3,4,8,1,2,5,9,6] => ([(0,4),(1,7),(1,8),(2,5),(2,6),(2,8),(3,5),(3,6),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,3,8,9,1,2,4,5,6] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9,8,4,5,1,2,3,6,7] => ([(0,7),(0,8),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [7,8,4,6,1,2,3,9,5] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9,8,6,5,1,2,3,4,7] => ([(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,6,1,2,3,4,5] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,6,5,1,2,3,9,4] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,9,6,1,7,2,4,5] => ([(0,3),(0,5),(0,8),(1,4),(1,6),(1,7),(1,8),(2,4),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,6,5,1,7,2,9,4] => ([(0,7),(1,6),(1,7),(1,8),(2,3),(2,6),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,6,4,5,1,7,2,9,3] => ([(0,7),(1,5),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [6,3,4,5,1,7,9,2,8] => ([(0,8),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,3,4,5,1,9,8,2,7] => ([(0,4),(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,5),(4,8),(5,8),(6,7),(7,8)],9)

[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [9,3,4,6,1,7,8,2,5] => ([(0,5),(0,7),(0,8),(1,5),(1,7),(1,8),(2,4),(2,7),(2,8),(3,4),(3,7),(3,8),(4,6),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,2] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)

[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,8,1,6,9,7] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)

[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [2,3,4,5,9,1,8,6,7] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(6,7),(7,8)],9)

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)

[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,9,6,1,5,7,8] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [2,3,4,9,7,1,5,6,8] => ([(0,8),(1,7),(2,7),(3,7),(4,6),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [2,3,4,9,6,1,8,5,7] => ([(0,7),(1,7),(2,7),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [2,3,4,9,7,1,8,5,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,3,9,5,6,1,4,7,8] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [2,3,8,5,6,1,4,9,7] => ([(0,7),(1,7),(2,3),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [2,3,9,5,6,1,8,4,7] => ([(0,7),(1,7),(2,5),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [2,8,4,5,6,1,3,9,7] => ([(0,7),(1,2),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,8,9,5,7,1,3,4,6] => ([(0,5),(1,6),(1,7),(1,8),(2,4),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,8,9,7,6,1,3,4,5] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,9,7,5,6,1,8,3,4] => ([(0,6),(1,4),(1,5),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [8,3,4,5,6,1,2,9,7] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,3,4,7,6,1,2,9,5] => ([(0,3),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,3,9,7,6,1,2,4,5] => ([(0,3),(0,4),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,3,7,5,6,1,2,9,4] => ([(0,6),(1,4),(1,5),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [9,7,4,5,6,1,2,3,8] => ([(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8,9,4,5,6,1,2,3,7] => ([(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,7,5,6,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,4,5,6,1,2,9,3] => ([(0,6),(1,3),(1,4),(1,5),(1,7),(1,8),(2,3),(2,4),(2,5),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,3,4,5,6,1,9,2,8] => ([(0,1),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9,3,4,5,6,1,8,2,7] => ([(0,5),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [9,3,7,5,6,1,8,2,4] => ([(0,5),(0,7),(0,8),(1,4),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,6),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,2] => ([(0,8),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,9,7,1,6,8] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,3,4,5,9,8,1,6,7] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [2,3,4,9,6,7,1,5,8] => ([(0,8),(1,8),(2,8),(3,7),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [2,3,9,5,6,7,1,4,8] => ([(0,8),(1,7),(2,7),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [2,3,9,5,6,8,1,4,7] => ([(0,7),(1,7),(2,6),(2,8),(3,5),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,9,4,5,6,7,1,3,8] => ([(0,8),(1,7),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [2,9,4,5,6,8,1,3,7] => ([(0,7),(1,5),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,9,4,5,8,7,1,3,6] => ([(0,7),(1,4),(1,7),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [2,9,4,8,6,7,1,3,5] => ([(0,7),(1,5),(1,7),(1,8),(2,3),(2,4),(2,6),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,9,8,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(1,7),(1,8),(2,3),(2,4),(2,5),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,8,4,5,6,7,1,9,3] => ([(0,8),(1,7),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9,3,4,5,6,8,1,2,7] => ([(0,5),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,2] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,9,8,1,7] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9)

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,5,9,7,8,1,6] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,9,6,7,8,1,5] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,9,5,6,7,8,1,4] => ([(0,8),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => ([(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(7,8)],9)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,2] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,1,2,9] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,1,4,5,6,7,8,9,2,3] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,1,2,10] => ([(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => ([(0,9),(1,8),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,10,2,9] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,10,5,6,7,8,9,2,4] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,10,3] => ([(0,9),(1,8),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [11,1,4,5,6,7,8,9,10,2,3] => ([(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,10),(9,10)],11)

[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)

[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [10,1,9,5,6,7,8,2,3,4] => ([(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,11,5,6,7,8,9,10,2,4] => ([(0,1),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [2,3,4,10,6,7,8,1,5,9] => ([(0,9),(1,9),(2,9),(3,8),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [11,1,10,5,6,7,8,9,2,3,4] => ([(0,10),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [2,3,4,5,10,7,8,1,6,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,1,10,9,6,7,8,2,4,5] => ([(0,1),(1,7),(2,4),(2,5),(2,6),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,6,10,8,1,7,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,3,1,5,6,7,8,10,2,9] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9,1,10,8,6,7,2,3,4,5] => ([(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [9,3,4,5,6,7,1,2,10,8] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10,1,11,9,6,7,8,2,3,4,5] => ([(0,10),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,10,1,5,6,7,8,9,3,4] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)

[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,8,11,1,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,11,2,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,8),(8,10),(9,10)],11)

[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [3,1,9,10,8,7,2,4,5,6] => ([(0,1),(1,5),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

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

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,10,7] => ([(0,7),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10,7,1,2,3,4,5,9,6,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,6),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8,7,1,2,3,4,5,9,10,6] => ([(0,7),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10,6,1,2,3,4,9,5,7,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,7),(4,9),(5,7),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10,7,1,2,3,4,9,5,6,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,10,1,2,3,4,8,5,6,7] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9,7,1,2,3,4,8,5,10,6] => ([(0,7),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,6,1,2,3,4,10,9,5,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,5),(4,6),(5,6),(5,7),(6,7),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10,7,1,2,3,4,8,9,5,6] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,9,1,2,3,7,8,4,5,6] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,8,7,3,4,5,6] => ([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10,3,1,9,2,4,5,6,7,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,6),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10,3,1,5,2,7,4,9,6,8] => ([(0,8),(0,9),(1,7),(1,9),(2,3),(2,4),(2,9),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,1,9,2,3,4,5,6,8] => ([(0,8),(0,9),(1,7),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,8,1,9,2,3,4,5,6,7] => ([(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,7,2,3,4,5,6] => ([(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [4,3,1,5,6,7,10,9,2,8] => ([(0,9),(1,9),(2,9),(3,7),(3,8),(4,5),(4,6),(5,6),(5,9),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [10,3,1,5,6,7,8,9,2,4] => ([(0,6),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,4,1,5,6,7,8,9,2,3] => ([(0,6),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,2] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,10,1,3,4,5,6,7,8] => ([(0,7),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9)],10)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,9,1,2,3,4,5,6,8] => ([(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [6,7,8,1,2,3,4,9,10,5] => ([(0,9),(1,9),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,1,6,2,3,4,10,5] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,3,4,1,6,10,8,9,2,7] => ([(0,9),(1,5),(1,6),(1,8),(2,3),(2,4),(2,7),(3,7),(3,9),(4,7),(4,9),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,2] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,10,5,1,7,4,9,6,8] => ([(0,8),(1,8),(2,7),(2,9),(3,4),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,10,6] => ([(0,6),(1,5),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,1,7,3,4,5,6] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10,8,4,9,1,2,3,5,6,7] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [7,8,9,5,1,2,3,4,10,6] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,6,1,2,3,4,10,5] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [10,3,4,5,1,7,8,9,2,6] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,8),(3,9),(4,6),(4,8),(4,9),(5,6),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,2] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [2,3,10,5,6,1,8,9,4,7] => ([(0,8),(1,8),(2,3),(2,4),(2,9),(3,7),(3,9),(4,7),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [2,8,9,10,6,1,3,4,5,7] => ([(0,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,7,1,3,4,5,6] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [8,3,4,9,10,1,2,5,6,7] => ([(0,5),(0,6),(0,9),(1,5),(1,6),(1,9),(2,5),(2,6),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [8,9,4,5,10,1,2,3,6,7] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,7,5,6,1,2,3,10,4] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,7,4,5,6,1,8,2,10,3] => ([(0,8),(1,6),(1,8),(1,9),(2,3),(2,4),(2,5),(2,7),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [10,3,4,7,6,1,8,9,2,5] => ([(0,5),(0,8),(0,9),(1,5),(1,8),(1,9),(2,4),(2,8),(2,9),(3,4),(3,8),(3,9),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,2] => ([(0,9),(1,9),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [2,3,4,5,10,7,1,9,6,8] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,8,6,7,1,3,4,5] => ([(0,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [2,10,8,5,6,7,1,9,3,4] => ([(0,7),(1,5),(1,6),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,3,8,5,6,7,1,2,10,4] => ([(0,7),(1,5),(1,6),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,10,3] => ([(0,7),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,1,9,2,8] => ([(0,6),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [10,3,8,5,6,7,1,9,2,4] => ([(0,6),(0,8),(0,9),(1,5),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,2] => ([(0,9),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [2,10,4,5,6,7,9,1,3,8] => ([(0,8),(1,6),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [2,10,4,9,6,7,8,1,3,5] => ([(0,8),(1,6),(1,8),(1,9),(2,3),(2,4),(2,5),(2,7),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [2,10,9,5,6,7,8,1,3,4] => ([(0,7),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,10,3] => ([(0,9),(1,8),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,9,1,2,8] => ([(0,6),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10,9,4,5,6,7,8,1,2,3] => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,10,9,1,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,10,8,9,1,7] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,1,6] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,10,6,7,8,9,1,5] => ([(0,9),(1,9),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,10,5,6,7,8,9,1,4] => ([(0,9),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,2] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => ([(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] => [9,1,2,3,4,5,6,7,10,8] => ([(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] => [10,1,2,3,4,5,6,9,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => ([(0,9),(1,9),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => ([(0,9),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => ([(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,1,2,3,4,5,6,7,10,8,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8)],10)

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [11,1,2,3,4,5,6,10,7,8,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,1,2,3,4,10,9,5,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8)],10)

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [10,1,2,3,4,5,11,6,7,8,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11)

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,1,2,3,9,10,4,6,7,8] => ([(0,7),(1,7),(2,7),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,4,10,5,6,7,8,9] => ([(0,10),(1,10),(2,10),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,10,9,3,5,6,7,8] => ([(0,7),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9),(8,9)],10)

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,10,4,5,6,7,8,9] => ([(0,10),(1,10),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,10,9,2,4,5,6,7,8] => ([(0,6),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => ([(0,10),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,10,2,3,4,5,6,7,8,9] => ([(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,1,2,3,4,5,6,7,8,9] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [12,1,2,3,4,5,6,7,8,11,9,10] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,11,10,1,3,4,5,6,7,8,9] => ([(0,8),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [10,1,2,9,6,3,4,5,7,8] => ([(0,9),(1,9),(2,8),(2,9),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(8,9)],10)

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,1,10,9,2,3,4,5,6,8] => ([(0,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(8,9)],10)

[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11,10,5,1,2,3,4,6,7,8,9] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,1,8,9,2,3,4,5,6,7] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)

[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,10,7,2,3,4,5,6] => ([(0,8),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,1,10,9,2,3,4,5,6,7,8] => ([(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,11,8,1,2,3,4,5,6,7,9] => ([(0,9),(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10)],11)

[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,10,11,2,3,4,5,6,7] => ([(0,10),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)

[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(7,9)],10)

[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)

[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)

[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,10,2,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(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] => [2,10,1,3,4,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,8,1,3,4,5,6,10,7,9] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)

[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)

[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)

[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(7,9)],10)

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(8,9)],10)

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(7,9)],10)

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,11,1,3,4,5,6,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,11,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,8),(8,10),(9,10)],11)

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,11,1,4,5,6,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)

[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,11,1,5,6,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(9,10)],11)

[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,11,5] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,11,1,6,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(9,10)],11)

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => ([(0,10),(1,10),(2,10),(3,10),(4,9),(5,9),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,11,1,7,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(9,10)],11)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,11,1,8,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,7,9,1,10,11,8] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(8,10)],11)

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => ([(0,9),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => ([(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,1,10,2,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,1,2,3,4,5,6,7,8,10] => ([(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,10,7,6,1,2,3,4,11,5] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,11,8,7,1,3,4,5,6] => ([(0,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,10,11,7,1,2,3,4,5,12,6] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,7),(3,8),(3,9),(3,10),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,11),(8,11),(9,11),(10,11)],12)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,11,6] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10)],11)

[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,11,1,3,4,5,6,7] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10)],11)

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,11,12,8,1,3,4,5,6,7] => ([(0,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,7),(3,8),(3,9),(3,10),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,11),(8,11),(9,11),(10,11)],12)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,10,1,3,4,5,6,9,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [10,9,1,2,3,4,5,6,7,11,8] => ([(0,8),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,11,2] => ([(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2,11,4,5,6,7,8,9,10,1,3] => ([(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,12,2] => ([(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(10,11)],12)

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10,9,4,5,6,7,8,1,2,11,3] => ([(0,8),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [2,11,10,5,6,7,8,9,1,3,4] => ([(0,8),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2,12,4,5,6,7,8,9,10,11,1,3] => ([(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(10,11)],12)

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,11,1,3,4,5,6,7,10,8,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,3,1,2,4,5,6,9,7,8] => ([(0,9),(1,9),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(5,9),(6,7),(6,9),(7,9),(8,9)],10)

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,10,2,4,5,6,9,7,8] => ([(0,9),(1,9),(2,9),(3,6),(4,8),(4,9),(5,8),(5,9),(6,7),(7,9),(8,9)],10)

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,3,1,2,4,5,6,7,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,8,1,2,3,4,5,6,9] => ([(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,7,10,1,2,3,4,5,8,9] => ([(0,9),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,10,5,1,2,3,4,7,8,9] => ([(0,9),(1,9),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [10,5,4,1,2,3,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,3,4,1,2,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(7,9),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,11,10,1,9] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(7,9),(8,9),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,9,12,11,1,10] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [11,3,4,5,6,7,8,10,1,2,9] => ([(0,7),(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,10),(9,10)],11)

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,5,10,7,1,6,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,4,10,6,1,5,7,8,9] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,8),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,10,5,1,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,2] => ([(0,8),(0,9),(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,10),(9,10)],11)

[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,11,2] => ([(0,10),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,11,2] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,9,1,2,3,4,5,10,8] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,1,9,10,3,4,5,6,7] => ([(0,1),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,7,1,10,2,3,4,5,6,9] => ([(0,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(8,9)],10)

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,11,1,9,2,3,4,5,6,7,8] => ([(0,9),(0,10),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [12,3,4,5,6,7,8,9,10,11,1,2] => ([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)

[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,3,1,2,6,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(7,8),(8,9)],10)

[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,3,4,1,2,7,8,9,10,5] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,3,4,5,1,2,8,9,10,6] => ([(0,6),(1,6),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [8,3,4,5,6,1,2,9,10,7] => ([(0,6),(1,6),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,5,2,3,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,2,5,3,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [11,1,2,3,4,5,8,6,7,9,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [11,1,2,3,4,5,9,6,7,8,10] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,9,1,2,3,4,6,7,10,8] => ([(0,7),(1,9),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,9)],10)

[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,10,1,5,3,4,6,7,8,9] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11,10,1,5,2,3,4,6,7,8,9] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [5,11,1,2,10,3,4,6,7,8,9] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,8),(4,10),(5,8),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(9,10)],11)

[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,11,1,2,3,10,4,6,7,8,9] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,8),(4,10),(5,8),(5,10),(6,8),(6,10),(7,8),(7,9),(7,10),(9,10)],11)

[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9,1,10,11,8,7,2,3,4,5,6] => ([(0,8),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)

[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [3,1,8,9,10,2,4,5,6,7] => ([(0,1),(1,6),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,10,8,1,3,4,5,6,7,9] => ([(0,9),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,1,8,2,3,4,5,6,10,7] => ([(0,9),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,7,1,2,3,4,5,6,10,8] => ([(0,7),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,10,1,9,3,4,5,6,7,8] => ([(0,7),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [8,6,1,2,3,4,5,9,10,7] => ([(0,7),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8,9,1,2,3,4,5,6,10,11,7] => ([(0,8),(1,8),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,7,1,2,3,4,8,9,10,6] => ([(0,8),(1,8),(2,8),(3,7),(3,9),(4,7),(4,9),(5,7),(5,9),(6,7),(6,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8,11,1,2,3,4,5,9,10,6,7] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,7),(5,8),(5,10),(6,7),(6,8),(6,10),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [10,4,1,2,3,7,8,9,5,6] => ([(0,6),(0,9),(1,6),(1,9),(2,6),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,4,8,9,5,6,7] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [10,3,1,2,9,7,8,4,5,6] => ([(0,2),(0,9),(1,2),(1,9),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,9,8,4,5,6,7] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,9,1,10,8,7,3,4,5,6] => ([(0,1),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,11,8,3,4,5,6,7] => ([(0,9),(0,10),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(8,9),(8,10),(9,10)],11)

[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,11,2,3,4,5,6,7] => ([(0,9),(0,10),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(9,10)],11)

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,8,9,10,1,2,3,4,5,6,7] => ([(0,7),(0,8),(0,9),(0,10),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,10),(8,10),(9,10)],11)

[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,6,1,5,3,7,8,9,10,4] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,8),(6,7),(6,8),(7,8),(7,9),(8,9)],10)

[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [5,3,4,1,6,7,9,2,10,8] => ([(0,9),(1,9),(2,3),(3,4),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(8,9)],10)

[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,8,1,6,7,4,9,10,5] => ([(0,8),(1,8),(2,4),(3,4),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3,4,5,1,8,2,9,10,7] => ([(0,6),(1,6),(2,6),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(7,8),(8,9)],10)

[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,10,1,7,8,9,5,6] => ([(0,6),(1,6),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [2,3,4,5,6,10,1,9,7,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(7,8),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,7,11,9,10,1,8] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,5,10,1,8,9,6,7] => ([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(4,9),(5,6),(5,7),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,6,11,8,9,10,1,7] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,11,7,8,9,10,1,6] => ([(0,10),(1,10),(2,10),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,10,1,6,7,8,9,4,5] => ([(0,6),(1,6),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [2,3,4,11,6,7,8,9,10,1,5] => ([(0,10),(1,10),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [2,3,11,5,6,7,8,9,10,1,4] => ([(0,10),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(9,10)],11)

[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,2,10,3,5,9,6,7,8] => ([(0,9),(1,7),(2,7),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(6,9),(8,9)],10)

[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,11,3] => ([(0,10),(1,9),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10)],11)

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,12,1] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)

[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,1,10,2,3,4,5,9,7,8] => ([(0,8),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(5,9),(6,7),(6,9),(7,9)],10)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => ([(0,11),(1,10),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12)

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,10,11,12,1,2,3,4,5,6,7] => ([(0,7),(0,8),(0,9),(0,10),(0,11),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,7),(3,8),(3,9),(3,10),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11)],12)

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,10,4,1,6,3,8,5,7,9] => ([(0,8),(1,9),(2,7),(2,9),(3,4),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [2,3,4,10,6,7,1,5,8,9] => ([(0,8),(1,8),(2,8),(3,9),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [2,3,10,5,6,1,4,7,8,9] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

graph of inversions

Description

The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.