- FindStat

Identifier

Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 974 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,4,8],[2,5],[3,7],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,5],[4,7],[6]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,5],[4,7],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,4],[5,7],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,4],[5,7],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,8],[2,5],[3,6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,5],[4,6],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,5],[4,6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,4],[5,6],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,7],[2,6],[3,8],[4]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,6],[3,8],[5]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,6],[4,8],[5]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,5],[3,8],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,5],[4,8],[6]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,5],[4,8],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,4],[5,8],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,4],[5,8],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,6],[2,7],[3,8],[4]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4,6],[2,7],[3,8],[5]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2,7],[4,8],[5]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,5],[2,7],[3,8],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,7],[4,8],[6]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,7],[4,8],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,7],[5,8],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,7],[5,8],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2,5],[4,8],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,5],[4,8],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2,4],[5,8],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,5],[2,6],[3,8],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,6],[4,8],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,6],[4,8],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,6],[5,8],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,3],[4,6],[5,8],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,4],[6,8],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,4],[6,8],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,5],[6,8],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,5],[6,8],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,3],[4,5],[6,8],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,5],[3,6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,5],[4,6],[8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,5],[4,6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,4],[5,6],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,4],[5,6],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,6],[2,5],[3,7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,5],[4,7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,3,6],[2,4],[5,7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,4],[5,7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,6],[4,7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,3,4],[2,6],[5,7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,6],[5,7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,4],[6,7],[8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,4],[6,7],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,5],[6,7],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,5],[6,7],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,3],[4,5],[6,7],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,6,8],[2,7],[3],[4],[5]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,8],[2,7],[3],[4],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,8],[2,7],[3],[5],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,7],[4],[5],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,8],[2,6],[3],[4],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,8],[2,6],[3],[5],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,6],[4],[5],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,6],[4],[5],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,8],[2,5],[3],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,5],[4],[6],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,5],[4],[6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2,4],[5],[6],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3,4],[5],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,7],[2,8],[3],[4],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,8],[3],[5],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,8],[4],[5],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,6],[2,8],[3],[4],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,6],[2,8],[3],[5],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2,8],[4],[5],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,8],[4],[5],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,5],[2,8],[3],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,8],[4],[6],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,8],[4],[6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,8],[5],[6],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,8],[5],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,3],[4,8],[5],[6],[7]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[[1,5,7],[2,6],[3],[4],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,6],[3],[5],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,6],[4],[5],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2,5],[3],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,5],[4],[6],[8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,5],[4],[6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2,4],[5],[6],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,7],[3,4],[5],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,6],[2,7],[3],[4],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4,6],[2,7],[3],[5],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2,7],[4],[5],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,5],[2,7],[3],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,5],[2,7],[4],[6],[8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,7],[4],[6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,4],[2,7],[5],[6],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,7],[5],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,6],[2,5],[3],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,5],[4],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,3,6],[2,4],[5],[7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,6],[3,4],[5],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3,6],[4],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,3,4],[2,6],[5],[7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,4],[3,6],[5],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,3],[4,5],[6],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,6,8],[2],[3],[4],[5],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,8],[2],[3],[4],[6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,8],[2],[3],[5],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,8],[2],[4],[5],[6],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,8],[3],[4],[5],[6],[7]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[[1,5,7],[2],[3],[4],[6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4,7],[2],[3],[5],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,7],[2],[4],[5],[6],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5,6],[2],[3],[4],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4,6],[2],[3],[5],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3,6],[2],[4],[5],[7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2,5],[3],[4],[6],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,2,3],[4],[5],[6],[7],[8]] => [8] => ([],8) => ([],8)

[[1,5],[2,6],[3,7],[4,8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4],[2,6],[3,7],[5,8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,6],[4,7],[5,8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,5],[3,7],[6,8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4,7],[6,8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,4],[5,7],[6,8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,4],[5,7],[6,8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,5],[3,6],[7,8]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,5],[4,6],[7,8]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4,6],[7,8]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,4],[5,6],[7,8]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,4],[5,6],[7,8]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5],[2,7],[3,8],[4],[6]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,7],[3,8],[5],[6]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,7],[4,8],[5],[6]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5],[2,6],[3,8],[4],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,6],[3,8],[5],[7]] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,6],[4,8],[5],[7]] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,6],[4,8],[5],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,5],[3,8],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,5],[4,8],[6],[7]] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4,8],[6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,4],[5,8],[6],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,4],[5,8],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5],[2,6],[3,7],[4],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4],[2,6],[3,7],[5],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,6],[4,7],[5],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,5],[3,7],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4,7],[6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,4],[5,7],[6],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,4],[5,7],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4,6],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,3],[2,4],[5,6],[7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,4],[5,6],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,6],[2,8],[3],[4],[5],[7]] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5],[2,8],[3],[4],[6],[7]] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,8],[3],[5],[6],[7]] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,8],[4],[5],[6],[7]] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,8],[4],[5],[6],[7]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[[1,5],[2,7],[3],[4],[6],[8]] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,4],[2,7],[3],[5],[6],[8]] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,7],[4],[5],[6],[8]] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,5],[2,6],[3],[4],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,4],[2,6],[3],[5],[7],[8]] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,3],[2,6],[4],[5],[7],[8]] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)

[[1,2],[3,5],[4],[6],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,8],[2],[3],[4],[5],[6],[7]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)

[[1,5],[2],[3],[4],[6],[7],[8]] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8)

[[1,2],[3],[4],[5],[6],[7],[8]] => [8] => ([],8) => ([],8)

[[1],[2],[3],[4],[5],[6],[7],[8]] => [8] => ([],8) => ([],8)

Map

valley composition

Description

The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.

Map

to threshold graph

Description

The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.

Map

Ore closure

Description

The Ore closure of a graph.
The Ore closure of a connected graph $G$ has the same vertices as $G$, and the smallest set of edges containing the edges of $G$ such that for any two vertices $u$ and $v$ whose sum of degrees is at least the number of vertices, then $(u,v)$ is also an edge.
For disconnected graphs, we compute the closure separately for each component.