Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-2Cc0010;cc-rep-3Cc0010;cc-rep-4Cc0020;cc-rep-5
[[1]]=>[1]=>[.,.]=>[.,.]=>[.,.]=>([],1)
[[1,2]]=>[1,2]=>[.,[.,.]]=>[[.,.],.]=>[[.,.],.]=>([(0,1)],2)
[[1],[2]]=>[2,1]=>[[.,.],.]=>[.,[.,.]]=>[.,[.,.]]=>([(0,1)],2)
[[1,2,3]]=>[1,2,3]=>[.,[.,[.,.]]]=>[[[.,.],.],.]=>[[[.,.],.],.]=>([(0,2),(1,2)],3)
[[1,3],[2]]=>[2,1,3]=>[[.,.],[.,.]]=>[[.,.],[.,.]]=>[[.,[.,.]],.]=>([(0,2),(1,2)],3)
[[1,2],[3]]=>[3,1,2]=>[[.,.],[.,.]]=>[[.,.],[.,.]]=>[[.,[.,.]],.]=>([(0,2),(1,2)],3)
[[1],[2],[3]]=>[3,2,1]=>[[[.,.],.],.]=>[.,[.,[.,.]]]=>[.,[.,[.,.]]]=>([(0,2),(1,2)],3)
[[1,2,3,4]]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>([(0,3),(1,2),(2,3)],4)
[[1,3,4],[2]]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4)
[[1,2,4],[3]]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4)
[[1,2,3],[4]]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2,4]]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3,4]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[2],[3]]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[4]]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3],[4]]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4)
[[1],[2],[3],[4]]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>([(0,3),(1,2),(2,3)],4)
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6],[2,8],[3],[7]]=>[7,3,2,8,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
searching the database
Sorry, this map was not found in the database.