Identifier
Values
[1,0] => [1] => ([],1) => ([],1) => 0
[1,0,1,0] => [1,2] => ([],2) => ([],1) => 0
[1,1,0,0] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 1
[1,0,1,0,1,0] => [1,2,3] => ([],3) => ([],1) => 0
[1,0,1,1,0,0] => [1,3,2] => ([(1,2)],3) => ([(1,2)],3) => 1
[1,1,0,0,1,0] => [2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 1
[1,1,0,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
[1,1,1,0,0,0] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => ([],4) => ([],1) => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => ([(2,3)],4) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => ([(2,3)],4) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 1
[1,1,1,0,1,0,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => ([],5) => ([],1) => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => ([(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => ([(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => ([(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => ([],6) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => ([(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => ([(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => ([(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 1
>>> Load all 271 entries. <<<
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,3),(1,2)],4) => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,3),(1,2)],4) => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,1)],2) => 1
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Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
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.
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.