Identifier
Values
[1,0,1,1,0,0,1,0] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[1,1,0,0,1,1,0,0] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
>>> Load all 436 entries. <<<
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => ([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => ([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => ([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => ([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => ([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => ([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => ([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => ([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => ([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => ([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => ([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => ([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => ([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => ([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => ([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => ([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => ([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => ([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => ([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => ([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => ([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => ([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => ([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => ([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(3,6),(4,1),(4,5)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => ([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => ([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => ([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => ([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => ([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => ([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => ([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => ([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => ([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => ([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => ([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => ([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => ([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => ([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => ([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => ([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => ([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => ([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => ([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => ([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => ([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => ([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => ([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => ([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => ([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => ([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => ([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => ([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => ([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => ([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => ([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => ([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => ([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => ([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => ([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => ([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => ([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => ([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => ([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => ([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => ([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => ([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => ([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => ([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => ([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => ([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => ([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => ([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => ([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => ([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => ([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => ([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => ([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => ([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => ([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => ([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => ([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => ([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7) => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => ([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => ([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => ([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => ([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => ([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => ([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => ([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7) => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => ([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => ([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => ([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],7) => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7) => ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => ([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => ([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => ([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => ([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => ([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => ([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => ([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => ([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => ([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => ([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => ([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => ([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => ([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 7
search for individual values
searching the database for the individual values of this statistic
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.