Identifier
Values
{{1}} => [1] => [1] => ([],1) => 0
{{1,2}} => [2,1] => [1,2] => ([],2) => 0
{{1},{2}} => [1,2] => [1,2] => ([],2) => 0
{{1,2,3}} => [2,3,1] => [1,2,3] => ([],3) => 0
{{1,2},{3}} => [2,1,3] => [1,2,3] => ([],3) => 0
{{1,3},{2}} => [3,2,1] => [1,3,2] => ([(1,2)],3) => 2
{{1},{2,3}} => [1,3,2] => [1,2,3] => ([],3) => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => ([],3) => 0
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => ([],4) => 0
{{1,2,3},{4}} => [2,3,1,4] => [1,2,3,4] => ([],4) => 0
{{1,2,4},{3}} => [2,4,3,1] => [1,2,4,3] => ([(2,3)],4) => 2
{{1,2},{3,4}} => [2,1,4,3] => [1,2,3,4] => ([],4) => 0
{{1,2},{3},{4}} => [2,1,3,4] => [1,2,3,4] => ([],4) => 0
{{1,3},{2,4}} => [3,4,1,2] => [1,3,2,4] => ([(2,3)],4) => 2
{{1,3},{2},{4}} => [3,2,1,4] => [1,3,2,4] => ([(2,3)],4) => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,2,3,4] => ([],4) => 0
{{1},{2,3},{4}} => [1,3,2,4] => [1,2,3,4] => ([],4) => 0
{{1},{2,4},{3}} => [1,4,3,2] => [1,2,4,3] => ([(2,3)],4) => 2
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,3,4] => ([],4) => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => ([],5) => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,3,4,5] => ([],5) => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5) => 2
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,2,3,4,5] => ([],5) => 0
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,2,3,4,5] => ([],5) => 0
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5) => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5) => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,2,3,4,5] => ([],5) => 0
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,2,3,4,5] => ([],5) => 0
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5) => 2
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,2,3,4,5] => ([],5) => 0
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,2,3,4,5] => ([],5) => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,3,2,4,5] => ([(3,4)],5) => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,3,2,4,5] => ([(3,4)],5) => 2
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 4
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,3,2,4,5] => ([(3,4)],5) => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,3,2,4,5] => ([(3,4)],5) => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,2,3,4,5] => ([],5) => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,2,3,4,5] => ([],5) => 0
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5) => 2
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,2,3,4,5] => ([],5) => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,2,3,4,5] => ([],5) => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5) => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5) => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,3,4,5] => ([],5) => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,3,4,5] => ([],5) => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5) => 2
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,4,5] => ([],5) => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 4
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 4
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 4
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 4
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 4
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [1,3,2,4,5,6] => ([(4,5)],6) => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
>>> Load all 381 entries. <<<
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 4
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,2,4,3,5,6] => ([(4,5)],6) => 2
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,3,5,4,6] => ([(4,5)],6) => 2
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,4,6,5] => ([(4,5)],6) => 2
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6) => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 4
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 4
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => 6
{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 2
{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
{{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 4
{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 6
{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 4
{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => 4
{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 2
{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 6
{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 4
{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 2
{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 4
{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 2
{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 2
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
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Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.