Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0010;cc-rep-0Cc0009;cc-rep-3
[.,.]=>[1]=>[1]=>{{1}}
[.,[.,.]]=>[2,1]=>[2,1]=>{{1,2}}
[[.,.],.]=>[1,2]=>[1,2]=>{{1},{2}}
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>{{1,3},{2}}
[.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>{{1,2,3}}
[[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>{{1,2,3}}
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}}
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>{{1,4},{2,3}}
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>{{1,2,3,4}}
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>{{1,4},{2},{3}}
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>{{1,3,4},{2}}
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>{{1,2,3,4}}
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>{{1,2,3,4}}
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>{{1,2,3,4}}
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>{{1,3,4},{2}}
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>{{1,2,3,4}}
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}}
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>{{1,2,3},{4}}
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>{{1,2,3},{4}}
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}}
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>{{1,2,4,5},{3}}
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>{{1,2,3,4,5}}
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}}
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>{{1,3,4,5},{2}}
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>{{1,2,3,4,5}}
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>{{1,2,4,5},{3}}
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>{{1,3,4},{2,5}}
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>{{1,2,3,5},{4}}
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>{{1,2,3,4,5}}
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>{{1,2,3,4,5}}
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>{{1,2,3,4,5}}
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>{{1,3,4,5},{2}}
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>{{1,3,5},{2,4}}
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>{{1,2,3,4,5}}
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>{{1,4,5},{2,3}}
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>{{1,4,5},{2},{3}}
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>{{1,2,3,4,5}}
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>{{1,3,4,5},{2}}
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>{{1,2,3,4,5}}
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}}
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>{{1,2,3,4},{5}}
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>{{1,2,3,4},{5}}
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>{{1,3,4},{2},{5}}
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}}
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}}
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}}
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}}
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}}
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}}
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}}
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}}
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}}
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>{{1,2,3,4,5,6}}
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>{{1,2,3,4,5,6}}
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}}
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>{{1,2,3,4,5,6}}
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}}
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}}
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}}
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}}
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}}
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}}
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}}
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}}
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>{{1,2,3,4,5,6}}
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}}
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}}
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}}
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}}
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}}
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}}
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}}
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}}
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}}
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}}
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}}
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}}
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}}
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}}
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}}
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}}
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}}
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}}
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}}
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}}
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}}
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}}
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}}
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}}
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}}
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}}
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}}
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}}
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}}
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}}
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}}
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}}
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}}
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}}
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}}
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}}
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}}
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}}
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}}
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}}
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}}
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}}
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}}
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}}
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}}
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}}
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}}
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}}
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}}
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}}
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}}
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}}
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}}
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}}
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}}
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}}
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}}
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}}
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}}
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}}
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}}
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}}
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}}
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}}
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}}
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}}
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}}
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}}
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}}
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}}
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}}
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}}
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}}
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}}
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}}
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}}
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}}
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}}
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}}
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}}
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}}
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}}
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}}
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}}
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}}
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}}
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}}
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}}
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}}
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}}
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}}
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}}
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}}
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}}
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}}
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}}
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}}
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}}
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}}
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}}
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}}
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}}
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}}
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}}
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}}
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}}
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}}
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}}
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}}
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}}
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}}
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}}
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}}
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}}
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}}
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}}
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}}
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}}
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}}
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}}
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}}
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}}
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}}
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}}
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}}
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}}
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}}
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}}
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}}
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}}
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}}
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}}
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}}
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}}
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}}
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}}
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}}
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}}
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}}
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}}
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}}
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}}
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}}
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}}
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}}
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}}
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}}
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}}
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}}
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}}
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}}
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}}
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}}
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}}
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}}
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}}
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}}
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}}
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}}
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}}
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}}
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}}
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}}
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}}
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}}
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}}
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}}
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}}
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}}
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}}
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}}
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}}
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}}
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}}
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}}
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}}
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}}
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}}
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}}
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}}
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}}
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}}
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}}
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}}
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1]=>{{1,2,7,8},{3,6},{4,5}}
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,6,7,5,4,3,2,1]=>{{1,8},{2,3,6,7},{4,5}}
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,6,8,5,4,3,2,1]=>{{1,2,3,6,7,8},{4,5}}
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,7,8,5,4,3,2,1]=>{{1,3,6,8},{2,7},{4,5}}
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[7,5,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,6,5,7,4,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,5,6,7,4,3,2,1]=>{{1,8},{2,4,5,7},{3,6}}
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>{{1,3,4,5,6,8},{2,7}}
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[7,5,6,8,4,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,5,7,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>{{1,4,5,8},{2,3,6,7}}
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>{{1,8},{2,7},{3,6},{4},{5}}
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,6,4,7,5,3,2,1]=>{{1,8},{2,3,4,6,7},{5}}
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[7,6,4,8,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[6,4,7,8,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[8,7,5,4,6,3,2,1]=>{{1,8},{2,7},{3,5,6},{4}}
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,4,5,6,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[7,4,5,8,6,3,2,1]=>{{1,2,4,7,8},{3,5,6}}
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,6,5,4,7,3,2,1]=>{{1,8},{2,3,5,6,7},{4}}
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[8,5,6,4,7,3,2,1]=>{{1,8},{2,5,7},{3,6},{4}}
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,6,4,5,7,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,4,5,6,7,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>{{1,3,5,6,8},{2,7},{4}}
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[7,5,6,4,8,3,2,1]=>{{1,2,5,7,8},{3,6},{4}}
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>{{1,5,8},{2,3,6,7},{4}}
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[7,6,4,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[6,4,7,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[7,5,4,6,8,3,2,1]=>{{1,2,5,7,8},{3,4,6}}
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[7,4,5,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>{{1,5,8},{2,3,4,6,7}}
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[6,4,5,7,8,3,2,1]=>{{1,3,5,6,8},{2,4,7}}
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>{{1,5,8},{2,4,7},{3,6}}
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>{{1,2,4,5,7,8},{3,6}}
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,6,5,3,4,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[7,8,6,3,5,4,2,1]=>{{1,2,7,8},{3,4,6},{5}}
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[8,6,7,3,5,4,2,1]=>{{1,8},{2,3,4,6,7},{5}}
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[7,6,8,3,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,5,3,6,4,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[7,5,3,8,6,4,2,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[6,7,3,5,8,4,2,1]=>{{1,4,5,6,8},{2,7},{3}}
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[3,5,7,6,8,4,2,1]=>[7,5,3,6,8,4,2,1]=>{{1,2,5,7,8},{3},{4,6}}
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,3,6,7,8,4,2,1]=>{{1,5,8},{2,3,4,6,7}}
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,7,6,4,3,5,2,1]=>{{1,8},{2,7},{3,5,6},{4}}
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[7,8,4,3,6,5,2,1]=>{{1,2,7,8},{3,4},{5,6}}
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[8,6,4,3,7,5,2,1]=>{{1,8},{2,5,6,7},{3,4}}
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[7,6,4,3,8,5,2,1]=>{{1,2,5,6,7,8},{3,4}}
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[6,4,3,7,8,5,2,1]=>{{1,5,6,8},{2,4,7},{3}}
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,3,4,5,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[3,4,7,8,6,5,2,1]=>[7,8,3,4,6,5,2,1]=>{{1,2,7,8},{3},{4},{5,6}}
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[6,3,4,7,8,5,2,1]=>{{1,5,6,8},{2,3,4,7}}
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>{{1,8},{2,7},{3,5},{4},{6}}
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[7,5,4,3,8,6,2,1]=>{{1,2,5,7,8},{3,4},{6}}
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[8,7,4,5,3,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[3,5,4,8,7,6,2,1]=>[8,7,5,3,4,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>[7,5,3,4,8,6,2,1]=>{{1,2,5,7,8},{3},{4},{6}}
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[8,7,4,3,5,6,2,1]=>{{1,8},{2,7},{3,4},{5},{6}}
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>{{1,8},{2,7},{3},{4},{5},{6}}
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[7,3,4,5,8,6,2,1]=>{{1,2,3,4,5,7,8},{6}}
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[8,6,5,4,3,7,2,1]=>{{1,8},{2,6,7},{3,5},{4}}
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[3,5,6,4,8,7,2,1]=>[8,5,3,6,4,7,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,6,4,3,5,7,2,1]=>{{1,8},{2,6,7},{3,4},{5}}
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[8,5,4,3,6,7,2,1]=>{{1,8},{2,5,6,7},{3,4}}
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[3,5,4,6,8,7,2,1]=>[8,5,3,4,6,7,2,1]=>{{1,8},{2,5,6,7},{3},{4}}
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[8,4,3,5,6,7,2,1]=>{{1,8},{2,4,5,6,7},{3}}
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[8,3,4,5,6,7,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,8,2,1]=>{{1,2,6,7,8},{3,5},{4}}
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[6,7,5,4,3,8,2,1]=>{{1,6,8},{2,7},{3,5},{4}}
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[7,5,6,4,3,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[6,5,7,4,3,8,2,1]=>{{1,6,8},{2,3,5,7},{4}}
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[5,6,7,4,3,8,2,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[7,5,4,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[4,5,7,6,3,8,2,1]=>[7,4,5,6,3,8,2,1]=>{{1,2,4,6,7,8},{3,5}}
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[6,5,4,7,3,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[4,6,5,7,3,8,2,1]=>[6,4,5,7,3,8,2,1]=>{{1,6,8},{2,4,7},{3,5}}
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>{{1,3,5,6,8},{2,4,7}}
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[7,6,5,3,4,8,2,1]=>{{1,2,6,7,8},{3,4,5}}
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[6,7,3,5,4,8,2,1]=>{{1,6,8},{2,7},{3},{4,5}}
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[6,5,3,7,4,8,2,1]=>{{1,6,8},{2,4,5,7},{3}}
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[5,3,6,7,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[7,6,4,3,5,8,2,1]=>{{1,2,6,7,8},{3,4},{5}}
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[7,6,3,4,5,8,2,1]=>{{1,2,6,7,8},{3},{4},{5}}
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[3,4,6,7,5,8,2,1]=>[6,3,4,7,5,8,2,1]=>{{1,6,8},{2,3,4,7},{5}}
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[7,5,4,3,6,8,2,1]=>{{1,2,5,6,7,8},{3,4}}
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[7,5,3,4,6,8,2,1]=>{{1,2,5,6,7,8},{3},{4}}
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[7,3,4,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>{{1,6,8},{2,5,7},{3,4}}
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[6,3,4,5,7,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[5,4,3,6,7,8,2,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>[5,3,4,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,8,2,1]=>{{1,4,6,8},{2,3,5,7}}
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[3,4,5,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,2,3,1]=>{{1,8},{2,3,6,7},{4,5}}
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[7,8,6,5,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,6,7,5,2,4,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[7,6,8,5,2,4,3,1]=>{{1,3,7,8},{2,4,5,6}}
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[6,7,8,2,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[8,6,5,7,2,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[8,5,6,2,7,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[7,6,5,8,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[6,7,5,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[7,5,6,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[6,5,7,2,8,4,3,1]=>{{1,2,4,5,6,8},{3,7}}
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,6,2,7,8,4,3,1]=>{{1,5,8},{2,3,4,6,7}}
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[7,8,4,2,6,5,3,1]=>{{1,2,3,4,7,8},{5,6}}
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,6,4,2,7,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[7,4,2,5,8,6,3,1]=>{{1,2,3,4,5,7,8},{6}}
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[8,6,5,4,2,7,3,1]=>{{1,8},{2,3,5,6,7},{4}}
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[8,5,6,2,4,7,3,1]=>{{1,8},{2,4,5},{3,6,7}}
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[8,4,2,5,6,7,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>[6,7,5,2,4,8,3,1]=>{{1,6,8},{2,3,4,5,7}}
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[7,6,4,2,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[6,4,2,7,5,8,3,1]=>{{1,6,8},{2,3,4,7},{5}}
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[7,5,4,2,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[6,5,4,2,7,8,3,1]=>{{1,6,8},{2,3,4,5,7}}
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[5,6,2,4,7,8,3,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[4,2,5,6,7,8,3,1]=>{{1,4,6,8},{2},{3,5,7}}
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,7,6,5,3,2,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[7,8,6,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[3,2,7,6,8,5,4,1]=>[7,6,8,3,2,5,4,1]=>{{1,3,4,7,8},{2,5,6}}
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[8,7,5,3,2,6,4,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[7,5,3,2,8,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[6,7,3,2,5,8,4,1]=>{{1,6,8},{2,4,7},{3},{5}}
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>{{1,8},{2,4,5,7},{3,6}}
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[2,3,7,8,6,5,4,1]=>[7,8,6,2,3,5,4,1]=>{{1,2,4,7,8},{3,5,6}}
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[8,6,7,2,3,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[6,7,2,3,8,5,4,1]=>{{1,5,6,8},{2,3,4,7}}
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[7,5,2,3,8,6,4,1]=>{{1,2,3,4,5,7,8},{6}}
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,5,2,3,6,7,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[7,5,2,3,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[2,3,6,5,7,8,4,1]=>[6,5,2,3,7,8,4,1]=>{{1,6,8},{2,3,4,5,7}}
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[5,2,3,6,7,8,4,1]=>{{1,4,5,6,7,8},{2},{3}}
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,7,6,4,3,2,5,1]=>{{1,8},{2,3,5,6,7},{4}}
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[7,8,4,3,2,6,5,1]=>{{1,2,5,7,8},{3,4},{6}}
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[6,4,3,2,7,8,5,1]=>{{1,6,8},{2,4},{3},{5,7}}
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,7,6,3,4,2,5,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[6,3,4,2,7,8,5,1]=>{{1,6,8},{2,3,4},{5,7}}
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,6,4,2,3,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[2,4,3,7,6,8,5,1]=>[7,6,4,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[6,4,2,3,7,8,5,1]=>{{1,6,8},{2,3,4},{5,7}}
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[8,7,6,3,2,4,5,1]=>{{1,8},{2,5,7},{3,4,6}}
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[3,2,4,7,8,6,5,1]=>[7,8,3,2,4,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[7,8,2,3,4,6,5,1]=>{{1,2,3,4,5,7,8},{6}}
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>[7,6,2,3,4,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,2,3,4,7,8,5,1]=>{{1,6,8},{2},{3},{4},{5,7}}
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,7,5,4,3,2,6,1]=>{{1,8},{2,6,7},{3,5},{4}}
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[7,5,4,3,2,8,6,1]=>{{1,6,7,8},{2,5},{3,4}}
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[7,4,5,3,2,8,6,1]=>{{1,6,7,8},{2,3,4,5}}
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,7,4,3,5,2,6,1]=>{{1,8},{2,6,7},{3,4},{5}}
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[8,7,5,4,2,3,6,1]=>{{1,8},{2,3,5,6,7},{4}}
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[8,7,4,2,5,3,6,1]=>{{1,8},{2,3,4,6,7},{5}}
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[7,5,2,3,4,8,6,1]=>{{1,6,7,8},{2,3,4,5}}
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,7,4,3,2,5,6,1]=>{{1,8},{2,5,6,7},{3,4}}
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[7,3,4,2,5,8,6,1]=>{{1,6,7,8},{2,3,4},{5}}
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[8,7,2,3,4,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[7,2,3,4,5,8,6,1]=>{{1,6,7,8},{2},{3},{4},{5}}
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>{{1,8},{2,6},{3,5},{4},{7}}
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[5,6,4,3,2,8,7,1]=>[8,5,6,4,3,2,7,1]=>{{1,8},{2,3,5,6},{4},{7}}
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[8,6,4,5,3,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[8,5,4,6,3,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[8,6,5,3,4,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>{{1,8},{2,6},{3,4},{5},{7}}
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[8,5,4,3,6,2,7,1]=>{{1,8},{2,5,6},{3,4},{7}}
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,4,5,3,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[8,3,4,5,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[8,6,5,4,2,3,7,1]=>{{1,8},{2,3,5,6},{4},{7}}
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,6,4,2,5,3,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[8,4,2,5,6,3,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,6,5,3,2,4,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[8,6,4,3,2,5,7,1]=>{{1,8},{2,5,6},{3,4},{7}}
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,6,4,2,3,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,6,2,3,4,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,5,4,3,2,6,7,1]=>{{1,8},{2,5},{3,4},{6},{7}}
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[8,4,5,3,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[3,5,4,2,6,8,7,1]=>[8,5,3,4,2,6,7,1]=>{{1,8},{2,5},{3},{4},{6},{7}}
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[8,3,4,5,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,5,4,2,3,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>[8,4,2,5,3,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>{{1,8},{2,4},{3},{5},{6},{7}}
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[8,3,4,2,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,4,2,3,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,7,1]=>{{1,8},{2,3},{4},{5},{6},{7}}
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,7,1]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,8,1]=>{{1,7,8},{2,6},{3,5},{4}}
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,7,5,4,3,2,8,1]=>{{1,2,6,7,8},{3,5},{4}}
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[7,5,6,4,3,2,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,5,7,4,3,2,8,1]=>{{1,2,3,5,6,7,8},{4}}
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[5,6,7,4,3,2,8,1]=>{{1,3,5,7,8},{2,6},{4}}
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[7,6,4,5,3,2,8,1]=>{{1,7,8},{2,6},{3,4,5}}
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>[6,4,7,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[7,4,5,6,3,2,8,1]=>{{1,7,8},{2,4,6},{3,5}}
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[6,5,4,7,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[6,4,5,7,3,2,8,1]=>{{1,2,4,6,7,8},{3,5}}
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>{{1,4,7,8},{2,3,5,6}}
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[7,6,5,3,4,2,8,1]=>{{1,7,8},{2,6},{3,4,5}}
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[7,5,3,6,4,2,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[5,3,6,7,4,2,8,1]=>{{1,4,5,7,8},{2,3,6}}
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[7,6,4,3,5,2,8,1]=>{{1,7,8},{2,6},{3,4},{5}}
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[7,6,3,4,5,2,8,1]=>{{1,7,8},{2,6},{3},{4},{5}}
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[7,5,4,3,6,2,8,1]=>{{1,7,8},{2,5,6},{3,4}}
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>[7,4,5,3,6,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>[7,3,4,5,6,2,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>{{1,2,5,6,7,8},{3,4}}
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[6,4,5,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>{{1,5,7,8},{2,3,4,6}}
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[4,5,6,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>{{1,2,5,6,7,8},{3},{4}}
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[5,3,6,4,7,2,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[6,4,3,5,7,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[6,3,4,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[5,4,3,6,7,2,8,1]=>{{1,5,7,8},{2,4,6},{3}}
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[4,5,3,6,7,2,8,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[4,3,5,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[3,4,5,6,7,2,8,1]=>{{1,3,5,7,8},{2,4,6}}
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[7,6,5,4,2,3,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[7,5,6,2,4,3,8,1]=>{{1,7,8},{2,4,5},{3,6}}
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[5,6,2,7,4,3,8,1]=>{{1,4,5,7,8},{2,3,6}}
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[6,4,2,7,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[7,5,4,2,6,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[7,4,2,5,6,3,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[5,6,2,4,7,3,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[5,4,2,6,7,3,8,1]=>{{1,5,7,8},{2,3,4,6}}
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[4,2,5,6,7,3,8,1]=>{{1,3,4,5,6,7,8},{2}}
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[6,7,3,2,5,4,8,1]=>{{1,2,4,6,7,8},{3},{5}}
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[7,5,3,2,6,4,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[6,5,3,2,7,4,8,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[5,3,2,6,7,4,8,1]=>{{1,5,7,8},{2,3},{4,6}}
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>{{1,7,8},{2,4,6},{3,5}}
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[5,2,3,6,7,4,8,1]=>{{1,5,7,8},{2},{3},{4,6}}
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[7,6,4,2,3,5,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[2,4,3,6,7,5,8,1]=>[6,4,2,3,7,5,8,1]=>{{1,5,6,7,8},{2,3,4}}
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[7,6,3,2,4,5,8,1]=>{{1,7,8},{2,4,5,6},{3}}
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[7,6,2,3,4,5,8,1]=>{{1,7,8},{2,3,4,5,6}}
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[7,5,4,3,2,6,8,1]=>{{1,7,8},{2,5},{3,4},{6}}
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[7,4,3,5,2,6,8,1]=>{{1,7,8},{2,4,5},{3},{6}}
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[7,5,4,2,3,6,8,1]=>{{1,7,8},{2,3,4,5},{6}}
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[7,5,3,2,4,6,8,1]=>{{1,7,8},{2,4,5},{3},{6}}
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[7,5,2,3,4,6,8,1]=>{{1,7,8},{2,3,4,5},{6}}
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[7,4,3,2,5,6,8,1]=>{{1,7,8},{2,4},{3},{5},{6}}
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[7,3,2,4,5,6,8,1]=>{{1,7,8},{2,3},{4},{5},{6}}
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[7,2,3,4,5,6,8,1]=>{{1,7,8},{2},{3},{4},{5},{6}}
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>{{1,6,7,8},{2,5},{3,4}}
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[4,5,6,3,2,7,8,1]=>{{1,3,4,6,7,8},{2,5}}
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>[6,3,4,5,2,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[4,3,5,6,2,7,8,1]=>{{1,4,6,7,8},{2,3,5}}
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[3,4,5,6,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[6,5,4,2,3,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[5,4,2,6,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[3,2,5,6,4,7,8,1]=>[5,3,2,6,4,7,8,1]=>{{1,4,5,6,7,8},{2,3}}
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[6,5,2,3,4,7,8,1]=>{{1,6,7,8},{2,3,4,5}}
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[6,2,3,4,5,7,8,1]=>{{1,6,7,8},{2},{3},{4},{5}}
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}}
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[4,5,3,2,6,7,8,1]=>{{1,2,4,5,6,7,8},{3}}
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[5,3,4,2,6,7,8,1]=>{{1,5,6,7,8},{2,3,4}}
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[4,3,5,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,5,2,6,7,8,1]=>{{1,3,5,6,7,8},{2,4}}
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[5,4,2,3,6,7,8,1]=>{{1,5,6,7,8},{2,3,4}}
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[4,2,5,3,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[5,3,2,4,6,7,8,1]=>{{1,5,6,7,8},{2,3},{4}}
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[5,2,3,4,6,7,8,1]=>{{1,5,6,7,8},{2},{3},{4}}
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,8,1]=>{{1,4,5,6,7,8},{2,3}}
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[4,2,3,5,6,7,8,1]=>{{1,4,5,6,7,8},{2},{3}}
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]=>{{1,2,7,8},{3,6},{4,5}}
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[7,8,6,5,4,1,3,2]=>{{1,3,6,7},{2,8},{4,5}}
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[8,6,7,5,4,1,3,2]=>{{1,2,6,8},{3,7},{4,5}}
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[7,6,8,5,4,1,3,2]=>{{1,2,3,6,7,8},{4,5}}
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[6,7,8,5,1,4,3,2]=>{{1,4,5,6},{2,3,7,8}}
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[8,7,5,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[7,5,8,6,1,4,3,2]=>{{1,2,3,5,7,8},{4,6}}
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[8,6,5,7,4,1,3,2]=>{{1,2,6,8},{3,4,5,7}}
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[8,5,6,7,1,4,3,2]=>{{1,2,5,8},{3,4,6,7}}
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[7,6,5,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[6,7,5,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[7,5,6,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[6,5,7,8,1,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,6,7,1,8,4,3,2]=>{{1,2,4,5,6,8},{3,7}}
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[8,7,6,4,5,1,3,2]=>{{1,2,3,6,7,8},{4},{5}}
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[8,6,4,7,1,5,3,2]=>{{1,2,5,6,8},{3,4,7}}
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[7,6,4,8,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,5,4,8,7,6,3,2]=>[8,7,5,4,6,1,3,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[7,5,4,8,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[8,7,4,5,1,6,3,2]=>{{1,2,3,4,5,7,8},{6}}
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[8,5,4,6,1,7,3,2]=>{{1,2,5,8},{3,4,6,7}}
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[7,6,5,4,8,1,3,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,6,7,5,4,8,3,2]=>[6,7,5,4,1,8,3,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[6,4,7,1,5,8,3,2]=>{{1,2,4,6,8},{3,7},{5}}
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,4,5,7,6,8,3,2]=>[7,4,5,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[5,4,6,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[4,5,1,6,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[8,7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[7,8,6,3,1,5,4,2]=>{{1,3,4,5,6,7},{2,8}}
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[7,6,8,3,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[6,7,3,1,8,5,4,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[8,7,5,3,1,6,4,2]=>{{1,2,3,4,5,7,8},{6}}
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[7,5,3,1,8,6,4,2]=>{{1,4,7},{2,5,8},{3},{6}}
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[7,6,5,3,1,8,4,2]=>{{1,3,4,5,7},{2,6,8}}
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[6,7,3,1,5,8,4,2]=>{{1,2,4,6,7,8},{3},{5}}
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[6,5,3,1,7,8,4,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[5,3,1,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[8,7,6,4,3,1,5,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[7,6,4,3,1,8,5,2]=>{{1,5,7},{2,6,8},{3,4}}
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[6,4,3,1,7,8,5,2]=>{{1,2,4,6,8},{3},{5,7}}
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[7,8,3,1,4,6,5,2]=>{{1,4,5,7},{2,8},{3},{6}}
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[8,6,3,1,4,7,5,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[8,7,5,4,3,1,6,2]=>{{1,2,6,7,8},{3,5},{4}}
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[7,5,4,3,1,8,6,2]=>{{1,2,5,6,7,8},{3,4}}
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[8,7,4,5,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,4,5,3,7,8,6,2]=>[7,4,5,1,3,8,6,2]=>{{1,2,4,6,7,8},{3,5}}
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[8,7,5,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[7,5,3,1,4,8,6,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[8,7,4,3,1,5,6,2]=>{{1,2,5,6,7,8},{3,4}}
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[7,4,3,1,5,8,6,2]=>{{1,2,4,6,7,8},{3},{5}}
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[8,7,3,1,4,5,6,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[8,6,5,4,3,1,7,2]=>{{1,2,6,8},{3,5},{4},{7}}
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[8,6,4,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,3,5,6,4,8,7,2]=>[8,5,3,1,6,4,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[8,6,4,3,1,5,7,2]=>{{1,2,5,6,8},{3,4},{7}}
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,3,4,6,5,8,7,2]=>[8,6,3,1,4,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[8,5,4,3,1,6,7,2]=>{{1,2,5,8},{3,4},{6},{7}}
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,3,5,4,6,8,7,2]=>[8,5,3,1,4,6,7,2]=>{{1,2,4,5,8},{3},{6},{7}}
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,4,3,5,6,8,7,2]=>[8,4,3,1,5,6,7,2]=>{{1,2,4,8},{3},{5},{6},{7}}
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[8,3,1,4,5,6,7,2]=>{{1,2,3,8},{4},{5},{6},{7}}
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[7,6,5,4,3,1,8,2]=>{{1,2,6,7,8},{3,5},{4}}
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,5,7,6,4,3,8,2]=>[7,5,6,4,1,3,8,2]=>{{1,2,5,7,8},{3,6},{4}}
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[6,5,7,4,1,3,8,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[7,6,4,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[6,4,7,1,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[7,4,5,1,6,3,8,2]=>{{1,2,4,7,8},{3,5,6}}
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,6,5,4,7,3,8,2]=>[6,5,4,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[5,6,4,1,7,3,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[5,4,6,1,7,3,8,2]=>{{1,2,4,5,7,8},{3,6}}
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[4,5,1,6,7,3,8,2]=>{{1,3,4,6},{2,5,7,8}}
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[7,5,3,1,6,4,8,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[5,3,1,6,7,4,8,2]=>{{1,2,3,5,7,8},{4,6}}
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[7,6,3,1,4,5,8,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[6,3,1,4,7,5,8,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[7,5,3,1,4,6,8,2]=>{{1,2,4,5,7,8},{3},{6}}
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[7,4,3,1,5,6,8,2]=>{{1,2,4,7,8},{3},{5},{6}}
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,3,4,5,7,6,8,2]=>[7,3,1,4,5,6,8,2]=>{{1,2,3,7,8},{4},{5},{6}}
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[6,5,4,3,1,7,8,2]=>{{1,2,5,6,7,8},{3,4}}
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[5,4,6,1,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[6,4,3,1,5,7,8,2]=>{{1,2,4,6,7,8},{3},{5}}
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[6,3,1,4,5,7,8,2]=>{{1,2,3,6,7,8},{4},{5}}
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[5,4,3,1,6,7,8,2]=>{{1,2,4,5,6,7,8},{3}}
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[4,5,1,3,6,7,8,2]=>{{1,3,4},{2,5,6,7,8}}
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[5,3,1,4,6,7,8,2]=>{{1,2,3,5,6,7,8},{4}}
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[4,3,1,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]=>{{1,2,3,6,7,8},{4,5}}
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[7,8,6,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[8,6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[7,6,8,5,2,1,4,3]=>{{1,2,4,5,6,7},{3,8}}
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[6,7,8,2,1,5,4,3]=>{{1,5,6},{2,4,7},{3,8}}
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[8,7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[7,5,8,2,1,6,4,3]=>{{1,2,4,5,7},{3,8},{6}}
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[8,6,5,7,2,1,4,3]=>{{1,2,3,5,6,8},{4,7}}
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[7,6,5,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[6,7,5,2,1,8,4,3]=>{{1,3,5,6,8},{2,4,7}}
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[7,5,6,2,1,8,4,3]=>{{1,2,4,5,7},{3,6,8}}
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[6,5,7,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>{{1,4,5,7},{2,3,6,8}}
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[8,7,6,4,2,1,5,3]=>{{1,3,6,8},{2,5,7},{4}}
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[7,8,4,2,1,6,5,3]=>{{1,5,7},{2,3,4,8},{6}}
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[8,6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[6,4,2,1,7,8,5,3]=>{{1,2,3,4,6,8},{5,7}}
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[8,7,5,4,2,1,6,3]=>{{1,2,3,5,6,7,8},{4}}
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[7,5,4,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[8,7,4,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[7,4,2,1,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[8,6,5,4,2,1,7,3]=>{{1,2,3,5,6,8},{4},{7}}
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[8,5,4,2,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[8,4,2,1,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[7,6,5,4,2,1,8,3]=>{{1,2,3,5,6,7,8},{4}}
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[6,5,7,2,1,4,8,3]=>{{1,2,4,5,6},{3,7,8}}
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[7,6,4,2,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[6,4,2,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[7,5,4,2,1,6,8,3]=>{{1,2,3,4,5,7,8},{6}}
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[6,5,4,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[5,6,2,1,4,7,8,3]=>{{1,4,5},{2,3,6,7,8}}
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[5,4,2,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[4,2,1,5,6,7,8,3]=>{{1,3,4,5,6,7,8},{2}}
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]=>{{1,3,6,8},{2,7},{4,5}}
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[7,8,6,5,1,2,4,3]=>{{1,4,5,7},{2,3,6,8}}
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[6,7,8,1,2,5,4,3]=>{{1,2,4,5,6,7},{3,8}}
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[8,7,5,6,1,2,4,3]=>{{1,3,5,8},{2,4,6,7}}
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[7,5,8,1,2,6,4,3]=>{{1,4,7},{2,5},{3,8},{6}}
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[8,5,6,1,2,7,4,3]=>{{1,3,4,6,7,8},{2,5}}
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[7,6,5,8,1,2,4,3]=>{{1,3,4,5,7,8},{2,6}}
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[7,5,6,1,2,8,4,3]=>{{1,4,7},{2,5},{3,6,8}}
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[5,6,1,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[8,7,6,4,1,2,5,3]=>{{1,2,3,5,6,7,8},{4}}
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[7,8,4,1,2,6,5,3]=>{{1,2,3,4,5,7,8},{6}}
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[8,6,4,1,2,7,5,3]=>{{1,3,4,8},{2,5,6,7}}
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[8,7,5,4,1,2,6,3]=>{{1,3,5,8},{2,6,7},{4}}
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[8,7,4,1,2,5,6,3]=>{{1,3,4,8},{2,5,6,7}}
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[8,6,5,4,1,2,7,3]=>{{1,3,5,8},{2,6},{4},{7}}
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[8,6,4,1,2,5,7,3]=>{{1,3,4,8},{2,5,6},{7}}
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[7,6,5,4,1,2,8,3]=>{{1,3,5,7,8},{2,6},{4}}
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[7,5,6,1,2,4,8,3]=>{{1,3,4,6,7,8},{2,5}}
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[5,6,1,2,7,4,8,3]=>{{1,3,5,7,8},{2,4,6}}
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[7,6,4,1,2,5,8,3]=>{{1,3,4,7,8},{2,5,6}}
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[6,4,1,2,7,5,8,3]=>{{1,3,5,6,7,8},{2,4}}
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,2,5,4,7,6,8,3]=>[7,5,4,1,2,6,8,3]=>{{1,3,4,7,8},{2,5},{6}}
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[6,5,4,1,2,7,8,3]=>{{1,3,4,6,7,8},{2,5}}
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[5,6,1,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[6,4,1,2,5,7,8,3]=>{{1,3,6,7,8},{2,4},{5}}
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[5,4,1,2,6,7,8,3]=>{{1,3,5,6,7,8},{2,4}}
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[7,8,6,3,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[7,6,8,3,2,1,5,4]=>{{1,2,5,6,7},{3,4,8}}
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[8,7,5,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[7,5,3,2,1,8,6,4]=>{{1,2,4,5,6,7,8},{3}}
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[8,6,5,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[8,5,3,2,1,6,7,4]=>{{1,2,4,5,8},{3},{6},{7}}
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[7,6,5,3,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[7,5,3,2,1,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[6,5,3,2,1,7,8,4]=>{{1,2,4,5,6,7,8},{3}}
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[5,3,2,1,6,7,8,4]=>{{1,4,5,6,7,8},{2,3}}
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[8,7,6,5,2,3,1,4]=>{{1,2,4,5,7,8},{3,6}}
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[8,6,7,2,3,1,5,4]=>{{1,2,4,6,8},{3,5,7}}
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[7,5,2,3,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[8,6,5,2,3,1,7,4]=>{{1,2,4,6,8},{3,5},{7}}
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[8,5,2,3,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[6,7,2,3,1,5,8,4]=>{{1,5,6},{2,3,4,7,8}}
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[7,5,2,3,1,6,8,4]=>{{1,2,3,4,5,7,8},{6}}
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[6,5,2,3,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[5,2,3,1,6,7,8,4]=>{{1,4,5,6,7,8},{2},{3}}
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]=>{{1,3,4,5,6,8},{2,7}}
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[7,8,6,3,1,2,5,4]=>{{1,5,7},{2,3,4,6,8}}
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[7,6,8,3,1,2,5,4]=>{{1,5,7},{2,6},{3,4,8}}
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[8,7,5,3,1,2,6,4]=>{{1,3,4,5,8},{2,6,7}}
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[7,5,3,1,2,8,6,4]=>{{1,4,6,7,8},{2,5},{3}}
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[8,6,5,3,1,2,7,4]=>{{1,3,4,5,8},{2,6},{7}}
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,3,2,5,6,8,7,4]=>[8,5,3,1,2,6,7,4]=>{{1,4,8},{2,5},{3},{6},{7}}
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[7,6,5,3,1,2,8,4]=>{{1,3,4,5,7,8},{2,6}}
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[6,5,3,1,2,7,8,4]=>{{1,4,6,7,8},{2,5},{3}}
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[5,3,1,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,5,4]=>{{1,5,7},{2,4,8},{3,6}}
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[8,6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[7,6,8,2,1,3,5,4]=>{{1,5,7},{2,3,4,6,8}}
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[6,7,2,1,3,8,5,4]=>{{1,4,6,8},{2,3,5,7}}
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[8,7,5,2,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[7,5,2,1,3,8,6,4]=>{{1,4,6,7,8},{2,3,5}}
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[6,5,2,1,3,7,8,4]=>{{1,4,6,7,8},{2,3,5}}
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[5,2,1,3,6,7,8,4]=>{{1,3,4,5,6,7,8},{2}}
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>{{1,4,5,8},{2,3,6,7}}
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[7,6,8,1,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[7,5,1,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[8,5,1,2,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[7,6,5,1,2,3,8,4]=>{{1,4,7,8},{2,3,5,6}}
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[6,7,1,2,3,5,8,4]=>{{1,3,5,6},{2,4,7,8}}
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[6,5,1,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]=>{{1,2,3,5,6,7,8},{4}}
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[7,8,4,3,2,1,6,5]=>{{1,6,7},{2,5,8},{3,4}}
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[8,6,4,3,2,1,7,5]=>{{1,2,5,6,8},{3,4},{7}}
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[7,6,4,3,2,1,8,5]=>{{1,2,5,6,7,8},{3,4}}
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[6,4,3,2,1,7,8,5]=>{{1,5,6,7,8},{2,4},{3}}
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[8,7,6,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[7,8,3,4,2,1,6,5]=>{{1,6,7},{2,5,8},{3},{4}}
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[7,6,3,4,2,1,8,5]=>{{1,2,5,6,7,8},{3},{4}}
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[6,3,4,2,1,7,8,5]=>{{1,5,6,7,8},{2,3,4}}
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[8,7,6,4,2,3,1,5]=>{{1,2,5,7,8},{3,6},{4}}
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[8,6,4,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[7,6,4,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[8,7,6,3,2,4,1,5]=>{{1,2,5,7,8},{3,4,6}}
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[7,8,3,2,4,1,6,5]=>{{1,6,7},{2,4,5,8},{3}}
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[8,6,3,2,4,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[7,6,3,2,4,1,8,5]=>{{1,2,4,5,6,7,8},{3}}
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[8,7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[7,8,2,3,4,1,6,5]=>{{1,6,7},{2,3,4,5,8}}
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[8,6,2,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[7,6,2,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[6,2,3,4,1,7,8,5]=>{{1,5,6,7,8},{2},{3},{4}}
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]=>{{1,3,5,6,8},{2,7},{4}}
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[7,6,4,3,1,2,8,5]=>{{1,5,7,8},{2,6},{3,4}}
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[6,4,3,1,2,7,8,5]=>{{1,2,4,5,6,7,8},{3}}
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[8,7,6,3,1,4,2,5]=>{{1,5,8},{2,7},{3,4,6}}
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[7,8,3,1,4,2,6,5]=>{{1,2,4,5,6,7,8},{3}}
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[8,6,3,1,4,2,7,5]=>{{1,4,5,8},{2,6},{3},{7}}
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[7,6,3,1,4,2,8,5]=>{{1,4,5,7,8},{2,6},{3}}
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[6,3,1,4,2,7,8,5]=>{{1,2,3,5,6,7,8},{4}}
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]=>{{1,2,3,5,6,7,8},{4}}
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[7,8,4,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[8,6,4,2,1,3,7,5]=>{{1,5,8},{2,3,4,6},{7}}
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[7,6,4,2,1,3,8,5]=>{{1,5,7,8},{2,3,4,6}}
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[6,4,2,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]=>{{1,5,8},{2,3,6,7},{4}}
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[7,8,4,1,2,3,6,5]=>{{1,3,4,6,7},{2,5,8}}
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[8,6,4,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[7,6,4,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[6,4,1,2,3,7,8,5]=>{{1,3,5,6,7,8},{2,4}}
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[7,8,3,2,1,4,6,5]=>{{1,2,4,5,6,7,8},{3}}
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[8,6,3,2,1,4,7,5]=>{{1,5,8},{2,4,6},{3},{7}}
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[6,3,2,1,4,7,8,5]=>{{1,4,5,6,7,8},{2,3}}
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[8,7,6,2,3,1,4,5]=>{{1,3,5,6,8},{2,4,7}}
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[6,2,3,1,4,7,8,5]=>{{1,4,5,6,7,8},{2},{3}}
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]=>{{1,5,8},{2,3,4,6,7}}
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,3,2,4,7,8,6,5]=>[7,8,3,1,2,4,6,5]=>{{1,4,6,7},{2,5,8},{3}}
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[8,6,3,1,2,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[7,6,3,1,2,4,8,5]=>{{1,2,4,5,6,7,8},{3}}
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[6,3,1,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]=>{{1,5,8},{2,4,7},{3,6}}
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[7,8,2,1,3,4,6,5]=>{{1,4,6,7},{2,3,5,8}}
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[6,2,1,3,4,7,8,5]=>{{1,3,4,5,6,7,8},{2}}
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>{{1,2,4,5,7,8},{3,6}}
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[7,8,1,2,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[8,6,1,2,3,4,7,5]=>{{1,3,5,8},{2,4,6},{7}}
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[7,6,1,2,3,4,8,5]=>{{1,3,5,7,8},{2,4,6}}
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]=>{{1,2,6,7,8},{3,5},{4}}
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[7,5,4,3,2,1,8,6]=>{{1,6,7,8},{2,5},{3,4}}
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[8,7,4,5,3,2,1,6]=>{{1,2,6,7,8},{3,4,5}}
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[8,7,5,3,4,2,1,6]=>{{1,2,6,7,8},{3,4,5}}
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[8,7,3,4,5,2,1,6]=>{{1,2,6,7,8},{3},{4},{5}}
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[7,5,4,2,3,1,8,6]=>{{1,6,7,8},{2,3,4,5}}
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[8,7,4,2,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[8,7,5,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[7,5,3,2,4,1,8,6]=>{{1,6,7,8},{2,4,5},{3}}
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[8,7,4,3,2,5,1,6]=>{{1,2,5,6,7,8},{3,4}}
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[8,7,3,4,2,5,1,6]=>{{1,2,5,6,7,8},{3},{4}}
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[7,4,2,3,5,1,8,6]=>{{1,6,7,8},{2,3,4},{5}}
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[7,3,2,4,5,1,8,6]=>{{1,6,7,8},{2,3},{4},{5}}
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[8,7,2,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[7,2,3,4,5,1,8,6]=>{{1,6,7,8},{2},{3},{4},{5}}
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]=>{{1,6,8},{2,7},{3,5},{4}}
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[8,7,4,5,1,3,2,6]=>{{1,3,4,5,6,8},{2,7}}
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,3,5,4,2,8,7,6]=>[8,7,5,3,1,4,2,6]=>{{1,3,4,5,6,8},{2,7}}
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[8,7,4,3,1,5,2,6]=>{{1,5,6,8},{2,7},{3,4}}
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[7,3,1,4,5,2,8,6]=>{{1,2,3,6,7,8},{4},{5}}
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[2,1,4,5,3,8,7,6]=>[8,7,4,2,1,5,3,6]=>{{1,5,6,8},{2,3,4,7}}
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[8,7,5,4,1,2,3,6]=>{{1,2,3,5,6,7,8},{4}}
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[7,5,4,1,2,3,8,6]=>{{1,3,4,6,7,8},{2,5}}
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[8,7,4,1,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[8,7,5,3,2,1,4,6]=>{{1,6,8},{2,3,4,5,7}}
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[2,3,1,5,4,7,8,6]=>[7,5,2,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[8,7,5,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[8,7,5,2,1,3,4,6]=>{{1,3,5,6,8},{2,4,7}}
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[7,5,1,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]=>{{1,6,8},{2,5,7},{3,4}}
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[7,4,3,2,1,5,8,6]=>{{1,5,6,7,8},{2,4},{3}}
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[8,7,3,4,2,1,5,6]=>{{1,6,8},{2,5,7},{3},{4}}
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[3,4,2,1,5,7,8,6]=>[7,3,4,2,1,5,8,6]=>{{1,5,6,7,8},{2,3,4}}
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[8,7,3,2,4,1,5,6]=>{{1,6,8},{2,4,5,7},{3}}
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[8,7,2,3,4,1,5,6]=>{{1,6,8},{2,3,4,5,7}}
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[7,2,3,4,1,5,8,6]=>{{1,5,6,7,8},{2},{3},{4}}
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[8,7,3,1,4,2,5,6]=>{{1,2,4,5,6,7,8},{3}}
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[7,3,1,4,2,5,8,6]=>{{1,2,3,5,6,7,8},{4}}
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[8,7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>[8,7,4,1,2,3,5,6]=>{{1,3,4,6,8},{2,5,7}}
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[7,4,1,2,3,5,8,6]=>{{1,3,5,6,7,8},{2,4}}
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]=>{{1,2,4,5,6,7,8},{3}}
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[7,3,2,1,4,5,8,6]=>{{1,4,5,6,7,8},{2,3}}
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[8,7,2,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[7,2,3,1,4,5,8,6]=>{{1,4,5,6,7,8},{2},{3}}
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[7,3,1,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]=>{{1,4,6,8},{2,3,5,7}}
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[7,2,1,3,4,5,8,6]=>{{1,3,4,5,6,7,8},{2}}
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,1,2,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]=>{{1,7,8},{2,6},{3,5},{4}}
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[8,5,6,4,3,2,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[8,6,4,5,3,2,1,7]=>{{1,7,8},{2,6},{3,4,5}}
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[8,4,5,6,3,2,1,7]=>{{1,7,8},{2,4,6},{3,5}}
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[8,6,5,3,4,2,1,7]=>{{1,7,8},{2,6},{3,4,5}}
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[8,4,5,3,6,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[8,4,3,5,6,2,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[8,3,4,5,6,2,1,7]=>{{1,7,8},{2,3,4,5,6}}
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[8,6,5,4,2,3,1,7]=>{{1,7,8},{2,3,5,6},{4}}
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[2,5,4,6,3,1,8,7]=>[8,5,4,2,6,3,1,7]=>{{1,7,8},{2,3,4,5,6}}
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[3,2,6,5,4,1,8,7]=>[8,6,5,3,2,4,1,7]=>{{1,7,8},{2,3,4,5,6}}
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[8,5,3,2,6,4,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[8,6,5,2,3,4,1,7]=>{{1,7,8},{2,4,6},{3,5}}
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[8,6,4,2,3,5,1,7]=>{{1,7,8},{2,3,4,5,6}}
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[3,2,4,6,5,1,8,7]=>[8,6,3,2,4,5,1,7]=>{{1,7,8},{2,4,5,6},{3}}
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[8,5,4,3,2,6,1,7]=>{{1,7,8},{2,5},{3,4},{6}}
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[8,4,3,5,2,6,1,7]=>{{1,7,8},{2,4,5},{3},{6}}
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[8,5,4,2,3,6,1,7]=>{{1,7,8},{2,3,4,5},{6}}
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[8,5,3,2,4,6,1,7]=>{{1,7,8},{2,4,5},{3},{6}}
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[8,3,4,2,5,6,1,7]=>{{1,7,8},{2,3,4},{5},{6}}
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[8,2,3,4,5,6,1,7]=>{{1,7,8},{2},{3},{4},{5},{6}}
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]=>{{1,2,6,7,8},{3,5},{4}}
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>[8,5,6,4,1,3,2,7]=>{{1,2,5,7,8},{3,6},{4}}
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,3,5,6,4,2,8,7]=>[8,5,3,1,6,4,2,7]=>{{1,2,4,5,6,7,8},{3}}
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]=>{{1,2,3,5,6,7,8},{4}}
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[8,5,6,2,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[8,6,4,2,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[8,5,4,2,1,6,3,7]=>{{1,2,3,4,5,7,8},{6}}
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[8,4,2,1,5,6,3,7]=>{{1,2,3,4,7,8},{5},{6}}
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[8,6,5,4,1,2,3,7]=>{{1,3,5,7,8},{2,6},{4}}
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,2,4,6,5,3,8,7]=>[8,6,4,1,2,5,3,7]=>{{1,3,4,7,8},{2,5,6}}
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,2,5,4,6,3,8,7]=>[8,5,4,1,2,6,3,7]=>{{1,3,4,7,8},{2,5},{6}}
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[8,4,1,2,5,6,3,7]=>{{1,3,7,8},{2,4},{5},{6}}
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[8,6,5,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[8,5,3,2,1,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[8,6,5,2,3,1,4,7]=>{{1,2,4,6,7,8},{3,5}}
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[2,3,1,5,6,4,8,7]=>[8,5,2,3,1,6,4,7]=>{{1,2,3,4,5,7,8},{6}}
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[8,6,5,2,1,3,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]=>{{1,4,7,8},{2,3,5,6}}
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[8,6,4,3,2,1,5,7]=>{{1,2,5,6,7,8},{3,4}}
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[8,6,3,4,2,1,5,7]=>{{1,2,5,6,7,8},{3},{4}}
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[8,6,4,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[8,6,3,2,4,1,5,7]=>{{1,2,4,5,6,7,8},{3}}
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[8,6,2,3,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[8,6,4,3,1,2,5,7]=>{{1,5,7,8},{2,6},{3,4}}
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[8,6,3,1,4,2,5,7]=>{{1,4,5,7,8},{2,6},{3}}
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[8,6,4,2,1,3,5,7]=>{{1,5,7,8},{2,3,4,6}}
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[8,6,4,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[8,6,3,2,1,4,5,7]=>{{1,5,7,8},{2,4,6},{3}}
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]=>{{1,3,5,7,8},{2,4,6}}
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[8,5,4,3,2,1,6,7]=>{{1,6,7,8},{2,5},{3,4}}
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[8,4,5,3,2,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[8,4,3,5,2,1,6,7]=>{{1,6,7,8},{2,4,5},{3}}
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[8,3,4,5,2,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[8,4,2,5,3,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[8,5,2,3,4,1,6,7]=>{{1,6,7,8},{2,3,4,5}}
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>[8,4,2,3,5,1,6,7]=>{{1,6,7,8},{2,3,4},{5}}
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[8,2,3,4,5,1,6,7]=>{{1,6,7,8},{2},{3},{4},{5}}
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[8,4,5,1,3,2,6,7]=>{{1,2,4,6,7,8},{3,5}}
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[8,5,4,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[8,4,2,1,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[8,5,4,1,2,3,6,7]=>{{1,3,4,6,7,8},{2,5}}
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[8,4,1,2,5,3,6,7]=>{{1,3,6,7,8},{2,4},{5}}
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[8,5,3,2,1,4,6,7]=>{{1,2,4,5,6,7,8},{3}}
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]=>[8,5,3,1,2,4,6,7]=>{{1,4,6,7,8},{2,5},{3}}
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[8,5,2,1,3,4,6,7]=>{{1,4,6,7,8},{2,3,5}}
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[8,5,1,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[8,4,3,2,1,5,6,7]=>{{1,5,6,7,8},{2,4},{3}}
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>[8,3,4,2,1,5,6,7]=>{{1,5,6,7,8},{2,3,4}}
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[8,2,3,4,1,5,6,7]=>{{1,5,6,7,8},{2},{3},{4}}
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[8,4,2,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]=>{{1,3,5,6,7,8},{2,4}}
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]=>{{1,4,5,6,7,8},{2,3}}
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[8,2,3,1,4,5,6,7]=>{{1,4,5,6,7,8},{2},{3}}
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[8,3,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[8,2,1,3,4,5,6,7]=>{{1,3,4,5,6,7,8},{2}}
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1,8]=>{{1,2,6,7},{3,5},{4},{8}}
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,5,6,4,3,2,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>{{1,3,5,7},{2,6},{4},{8}}
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,4,5,3,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[6,4,7,5,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[7,5,4,6,3,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[5,6,4,7,3,2,1,8]=>{{1,3,4,5,7},{2,6},{8}}
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[5,4,6,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,5,6,7,3,2,1,8]=>{{1,4,7},{2,3,5,6},{8}}
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[7,6,5,3,4,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,5,3,6,4,2,1,8]=>{{1,7},{2,4,5,6},{3},{8}}
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[7,6,4,3,5,2,1,8]=>{{1,7},{2,6},{3,4},{5},{8}}
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>{{1,7},{2,6},{3},{4},{5},{8}}
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>[7,5,4,3,6,2,1,8]=>{{1,7},{2,5,6},{3,4},{8}}
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[6,5,4,3,7,2,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[5,6,4,3,7,2,1,8]=>{{1,5,7},{2,6},{3,4},{8}}
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[5,4,6,3,7,2,1,8]=>{{1,5,7},{2,3,4,6},{8}}
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[5,3,6,4,7,2,1,8]=>{{1,5,7},{2,3,6},{4},{8}}
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[5,4,3,6,7,2,1,8]=>{{1,5,7},{2,4,6},{3},{8}}
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[3,4,5,6,7,2,1,8]=>{{1,3,5,7},{2,4,6},{8}}
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,6,5,4,2,3,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[2,6,5,7,4,3,1,8]=>[6,5,7,2,4,3,1,8]=>{{1,3,6,7},{2,4,5},{8}}
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[5,6,2,7,4,3,1,8]=>{{1,4,5,7},{2,3,6},{8}}
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[7,6,4,2,5,3,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[6,4,2,7,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[7,4,2,5,6,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,6,5,3,2,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[6,7,3,2,5,4,1,8]=>{{1,2,4,6,7},{3},{5},{8}}
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[3,2,6,5,7,4,1,8]=>[6,5,3,2,7,4,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[5,3,2,6,7,4,1,8]=>{{1,5,7},{2,3},{4,6},{8}}
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>{{1,7},{2,4,6},{3,5},{8}}
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[7,6,4,3,2,5,1,8]=>{{1,7},{2,5,6},{3,4},{8}}
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[2,4,3,7,6,5,1,8]=>[7,6,4,2,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[3,2,4,7,6,5,1,8]=>[7,6,3,2,4,5,1,8]=>{{1,7},{2,4,5,6},{3},{8}}
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[6,3,2,4,7,5,1,8]=>{{1,5,6,7},{2,3},{4},{8}}
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,5,4,3,2,6,1,8]=>{{1,7},{2,5},{3,4},{6},{8}}
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,4,5,3,2,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>{{1,7},{2,4,5},{3},{6},{8}}
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>{{1,7},{2,4,5},{3},{6},{8}}
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[2,4,3,5,7,6,1,8]=>[7,4,2,3,5,6,1,8]=>{{1,7},{2,3,4},{5},{6},{8}}
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,6,1,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[6,5,4,3,2,7,1,8]=>{{1,6,7},{2,5},{3,4},{8}}
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[5,6,4,3,2,7,1,8]=>{{1,2,5,6,7},{3,4},{8}}
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[5,4,6,3,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[5,3,6,4,2,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[6,3,4,5,2,7,1,8]=>{{1,6,7},{2,3,4,5},{8}}
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[5,4,3,6,2,7,1,8]=>{{1,2,4,5,6,7},{3},{8}}
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1,8]=>{{1,4,6,7},{2,5},{3},{8}}
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[5,3,4,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[4,3,5,6,2,7,1,8]=>{{1,4,6,7},{2,3,5},{8}}
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[3,4,5,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[2,4,6,5,3,7,1,8]=>[6,4,2,5,3,7,1,8]=>{{1,6,7},{2,3,4,5},{8}}
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[5,4,2,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[6,5,3,2,4,7,1,8]=>{{1,6,7},{2,4,5},{3},{8}}
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[6,4,2,3,5,7,1,8]=>{{1,6,7},{2,3,4},{5},{8}}
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[6,3,2,4,5,7,1,8]=>{{1,6,7},{2,3},{4},{5},{8}}
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[6,2,3,4,5,7,1,8]=>{{1,6,7},{2},{3},{4},{5},{8}}
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}}
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,4,5,2,6,7,1,8]=>{{1,3,5,6,7},{2,4},{8}}
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[5,4,2,3,6,7,1,8]=>{{1,5,6,7},{2,3,4},{8}}
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[5,2,3,4,6,7,1,8]=>{{1,5,6,7},{2},{3},{4},{8}}
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[4,3,2,5,6,7,1,8]=>{{1,4,5,6,7},{2,3},{8}}
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[3,4,2,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[2,4,3,5,6,7,1,8]=>[4,2,3,5,6,7,1,8]=>{{1,4,5,6,7},{2},{3},{8}}
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]=>{{1,2,6,7},{3,5},{4},{8}}
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,5,7,6,4,3,2,8]=>[7,5,6,4,1,3,2,8]=>{{1,2,5,7},{3,6},{4},{8}}
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[6,5,7,4,1,3,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,4,6,7,5,3,2,8]=>[6,4,7,1,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>[7,5,4,6,1,3,2,8]=>{{1,2,5,7},{3,4,6},{8}}
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[4,5,1,6,7,3,2,8]=>{{1,3,4,6},{2,5,7},{8}}
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[7,6,5,3,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[6,7,3,1,5,4,2,8]=>{{1,4,6},{2,7},{3},{5},{8}}
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[7,5,3,1,6,4,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,4,3,7,6,5,2,8]=>[7,6,4,3,1,5,2,8]=>{{1,2,5,6,7},{3,4},{8}}
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[6,3,1,4,7,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[7,4,3,1,5,6,2,8]=>{{1,2,4,7},{3},{5},{6},{8}}
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[7,3,1,4,5,6,2,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[5,4,6,1,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[4,5,1,6,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[6,5,3,1,4,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[5,3,1,6,4,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[6,4,3,1,5,7,2,8]=>{{1,2,4,6,7},{3},{5},{8}}
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[5,4,3,1,6,7,2,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[3,1,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[7,6,5,4,2,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[7,6,4,2,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[6,4,2,1,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[2,1,5,4,7,6,3,8]=>[7,5,4,2,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[2,1,4,5,7,6,3,8]=>[7,4,2,1,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[2,1,6,5,4,7,3,8]=>[6,5,4,2,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[2,1,4,6,5,7,3,8]=>[6,4,2,1,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[5,4,2,1,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[2,1,4,5,6,7,3,8]=>[4,2,1,5,6,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]=>{{1,3,5,7},{2,6},{4},{8}}
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[7,6,4,1,2,5,3,8]=>{{1,3,4,7},{2,5,6},{8}}
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,2,4,5,7,6,3,8]=>[7,4,1,2,5,6,3,8]=>{{1,3,7},{2,4},{5},{6},{8}}
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[6,4,1,2,5,7,3,8]=>{{1,3,6,7},{2,4},{5},{8}}
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[5,4,1,2,6,7,3,8]=>{{1,3,5,6,7},{2,4},{8}}
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[4,1,2,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[7,6,5,3,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[7,5,3,2,1,6,4,8]=>{{1,2,4,5,7},{3},{6},{8}}
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8]=>[7,6,5,2,3,1,4,8]=>{{1,2,4,6,7},{3,5},{8}}
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[6,7,2,3,1,5,4,8]=>{{1,5,6},{2,3,4,7},{8}}
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[6,5,3,1,2,7,4,8]=>{{1,4,6,7},{2,5},{3},{8}}
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]=>[7,6,5,2,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>{{1,4,7},{2,3,5,6},{8}}
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[5,1,2,3,6,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[7,6,4,3,2,1,5,8]=>{{1,2,5,6,7},{3,4},{8}}
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[6,4,3,2,1,7,5,8]=>{{1,5,6,7},{2,4},{3},{8}}
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[7,6,3,2,4,1,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[7,6,2,3,4,1,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[7,6,4,3,1,2,5,8]=>{{1,5,7},{2,6},{3,4},{8}}
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[6,4,3,1,2,7,5,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[7,6,3,1,4,2,5,8]=>{{1,4,5,7},{2,6},{3},{8}}
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[6,3,1,4,2,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]=>[7,6,4,2,1,3,5,8]=>{{1,5,7},{2,3,4,6},{8}}
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[7,6,3,2,1,4,5,8]=>{{1,5,7},{2,4,6},{3},{8}}
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[6,3,2,1,4,7,5,8]=>{{1,4,5,6,7},{2,3},{8}}
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]=>{{1,3,5,7},{2,4,6},{8}}
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[6,1,2,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[7,5,4,3,2,1,6,8]=>{{1,6,7},{2,5},{3,4},{8}}
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[7,4,5,3,2,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[7,4,3,5,2,1,6,8]=>{{1,6,7},{2,4,5},{3},{8}}
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[7,3,4,5,2,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[7,5,4,2,3,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[7,4,2,5,3,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[7,5,3,2,4,1,6,8]=>{{1,6,7},{2,4,5},{3},{8}}
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[7,5,2,3,4,1,6,8]=>{{1,6,7},{2,3,4,5},{8}}
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[7,4,2,3,5,1,6,8]=>{{1,6,7},{2,3,4},{5},{8}}
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[7,2,3,4,5,1,6,8]=>{{1,6,7},{2},{3},{4},{5},{8}}
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[7,5,4,3,1,2,6,8]=>{{1,2,5,6,7},{3,4},{8}}
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[7,5,3,1,4,2,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[7,3,1,4,5,2,6,8]=>{{1,2,3,6,7},{4},{5},{8}}
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[7,5,3,2,1,4,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[7,5,2,3,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[7,5,3,1,2,4,6,8]=>{{1,4,6,7},{2,5},{3},{8}}
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[7,5,1,2,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]=>{{1,5,6,7},{2,4},{3},{8}}
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[7,2,3,4,1,5,6,8]=>{{1,5,6,7},{2},{3},{4},{8}}
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[7,4,3,1,2,5,6,8]=>{{1,2,4,5,6,7},{3},{8}}
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>[7,4,1,2,3,5,6,8]=>{{1,3,5,6,7},{2,4},{8}}
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[7,3,2,1,4,5,6,8]=>{{1,4,5,6,7},{2,3},{8}}
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[7,2,3,1,4,5,6,8]=>{{1,4,5,6,7},{2},{3},{8}}
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[7,2,1,3,4,5,6,8]=>{{1,3,4,5,6,7},{2},{8}}
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}}
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[5,6,4,3,2,1,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[5,4,6,3,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[4,5,6,3,2,1,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>{{1,6},{2,5},{3},{4},{7},{8}}
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[3,5,6,4,2,1,7,8]=>[5,3,6,4,2,1,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[5,4,3,6,2,1,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[3,4,5,6,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[6,4,2,5,3,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[5,4,2,6,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>[6,5,2,3,4,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>{{1,6},{2,4},{3},{5},{7},{8}}
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[4,3,5,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,4,5,2,6,1,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[3,2,5,4,6,1,7,8]=>[5,3,2,4,6,1,7,8]=>{{1,5,6},{2,3},{4},{7},{8}}
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[5,2,3,4,6,1,7,8]=>{{1,5,6},{2},{3},{4},{7},{8}}
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[4,3,2,5,6,1,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[3,4,2,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[2,4,3,5,6,1,7,8]=>[4,2,3,5,6,1,7,8]=>{{1,4,5,6},{2},{3},{7},{8}}
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[3,2,4,5,6,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[6,5,4,3,1,2,7,8]=>{{1,2,5,6},{3,4},{7},{8}}
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[5,4,6,1,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[4,5,1,6,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[6,5,3,1,4,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[5,3,1,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>{{1,2,4,6},{3},{5},{7},{8}}
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[5,4,3,1,6,2,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[5,3,1,4,6,2,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[5,6,2,1,4,3,7,8]=>{{1,4,5},{2,3,6},{7},{8}}
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[2,1,5,4,6,3,7,8]=>[5,4,2,1,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[6,5,4,1,2,3,7,8]=>{{1,3,4,6},{2,5},{7},{8}}
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[6,4,1,2,5,3,7,8]=>{{1,3,6},{2,4},{5},{7},{8}}
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[4,1,2,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[6,5,3,2,1,4,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[5,3,2,1,6,4,7,8]=>{{1,4,5,6},{2,3},{7},{8}}
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[5,1,2,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[3,4,2,1,6,5,7,8]=>[6,3,4,2,1,5,7,8]=>{{1,5,6},{2,3,4},{7},{8}}
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[6,4,3,1,2,5,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[6,4,2,1,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[6,4,1,2,3,5,7,8]=>{{1,3,5,6},{2,4},{7},{8}}
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[6,3,1,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[6,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}}
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>{{1,5},{2,3},{4},{6},{7},{8}}
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>{{1,4,5},{2,3},{6},{7},{8}}
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>{{1,4,5},{2},{3},{6},{7},{8}}
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[4,5,1,3,2,6,7,8]=>{{1,3,4},{2,5},{6},{7},{8}}
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[5,3,1,4,2,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[5,4,2,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[4,2,1,5,3,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>{{1,4,5},{2,3},{6},{7},{8}}
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>{{1,4,5},{2},{3},{6},{7},{8}}
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>{{1,3,4,5},{2},{6},{7},{8}}
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>{{1,9},{2,8},{3,7},{4,6},{5}}
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[8,9,7,6,5,4,3,2,1]=>{{1,2,8,9},{3,7},{4,6},{5}}
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,8,9,6,5,4,3,2,1]=>{{1,3,7,9},{2,8},{4,6},{5}}
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1]=>{{1,4,6,9},{2,3,7,8},{5}}
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[5,6,7,8,9,4,3,2,1]=>{{1,5,9},{2,4,6,8},{3,7}}
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[4,5,6,7,8,9,3,2,1]=>{{1,3,4,6,7,9},{2,5,8}}
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[3,4,5,6,7,8,9,2,1]=>{{1,3,5,7,9},{2,4,6,8}}
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[9,10,8,7,6,5,4,3,2,1]=>{{1,2,9,10},{3,8},{4,7},{5,6}}
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[9,7,8,6,5,4,3,2,1]=>{{1,9},{2,3,7,8},{4,6},{5}}
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[8,9,10,7,6,5,4,3,2,1]=>{{1,3,8,10},{2,9},{4,7},{5,6}}
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[6,8,9,7,5,4,3,2,1]=>[8,6,9,7,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[7,8,9,10,6,5,4,3,2,1]=>{{1,4,7,10},{2,3,8,9},{5,6}}
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,10,5,4,3,2,1]=>{{1,5,6,10},{2,4,7,9},{3,8}}
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[5,6,7,8,9,10,4,3,2,1]=>{{1,2,5,6,9,10},{3,4,7,8}}
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[4,5,6,7,8,9,10,3,2,1]=>{{1,4,7,10},{2,3,5,6,8,9}}
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>[4,2,5,6,7,8,9,3,1]=>{{1,3,4,5,6,7,8,9},{2}}
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[3,4,5,6,7,8,9,10,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[3,1,4,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[8,7,9,6,5,4,3,2,1]=>{{1,2,3,7,8,9},{4,6},{5}}
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,9,5,4,3,2,1]=>{{1,2,3,4,6,7,8,9},{5}}
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,9,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,9,3,2,1]=>{{1,2,3,6,7,8,9},{4,5}}
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,9,2,1]=>{{1,2,7,8,9},{3,6},{4,5}}
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,9,1]=>{{1,8,9},{2,7},{3,6},{4,5}}
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>{{1,8},{2,7},{3,6},{4,5},{9}}
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[9,8,10,7,6,5,4,3,2,1]=>{{1,2,3,8,9,10},{4,7},{5,6}}
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1]=>[8,6,7,9,5,4,3,2,1]=>{{1,2,4,6,8,9},{3,7},{5}}
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,10,6,5,4,3,2,1]=>{{1,2,3,4,7,8,9,10},{5,6}}
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1]=>[8,7,5,6,9,4,3,2,1]=>{{1,2,3,5,7,8,9},{4,6}}
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,10,5,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1]=>[8,7,6,4,5,9,3,2,1]=>{{1,2,3,6,7,8,9},{4},{5}}
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,10,4,3,2,1]=>{{1,2,3,4,6,7,8,9,10},{5}}
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1]=>[8,7,6,5,3,4,9,2,1]=>{{1,2,7,8,9},{3,4,5,6}}
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,10,3,2,1]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1]=>[8,7,6,5,4,2,3,9,1]=>{{1,8,9},{2,3,6,7},{4,5}}
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,10,2,1]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]=>{{1,2,7,8},{3,6},{4,5},{9}}
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[9,8,7,6,5,4,3,2,10,1]=>{{1,9,10},{2,8},{3,7},{4,6},{5}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10}}
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,3,5,7,9,10,8,6,4,2]=>[9,7,5,3,1,10,8,6,4,2]=>{{1,3,4,5,9},{2,6,7,8,10}}
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[5,6,4,7,3,8,2,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[10,8,6,4,2,1,3,5,7,9]=>{{1,3,6,7,9,10},{2,5,8},{4}}
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[10,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[9,2,1,3,4,5,6,7,8]=>{{1,3,4,5,6,7,8,9},{2}}
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>[10,2,1,3,4,5,6,7,8,9]=>{{1,3,4,5,6,7,8,9,10},{2}}
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>[9,3,1,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>[9,2,3,1,4,5,6,7,8]=>{{1,4,5,6,7,8,9},{2},{3}}
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>[4,2,3,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2},{3}}
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,4,2,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}}
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[8,1,2,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[7,1,2,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[6,1,2,3,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[5,1,2,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[4,1,2,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]=>{{1,3,5,7,9},{2,4,6,8}}
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[9,1,2,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[8,7,1,2,3,4,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[8,1,2,3,4,5,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>[7,6,1,2,3,4,8,9,5]=>{{1,3,5,7,8,9},{2,4,6}}
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[7,1,2,3,4,5,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>[6,5,1,2,3,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[6,1,2,3,4,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>[5,4,1,2,6,7,8,9,3]=>{{1,3,5,6,7,8,9},{2,4}}
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[5,1,2,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[4,3,1,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[4,1,2,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[3,1,4,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]=>{{1,2,8,9},{3,7},{4,6},{5}}
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,8,6,5,4,3,2,1,9]=>{{1,2,7,8},{3,6},{4,5},{9}}
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[8,9,7,6,5,4,1,3,2]=>{{1,3,7,8},{2,9},{4,6},{5}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]=>{{1,2,9,10},{3,8},{4,7},{5,6}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11}}
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[8,9,7,6,5,4,3,2,1,10]=>{{1,2,8,9},{3,7},{4,6},{5},{10}}
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,6,8,5,4,3,2,1,9]=>{{1,2,3,6,7,8},{4,5},{9}}
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[8,7,9,6,5,4,1,3,2]=>{{1,2,3,7,8,9},{4,6},{5}}
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[9,10,8,7,6,5,4,1,3,2]=>{{1,3,8,9},{2,10},{4,7},{5,6}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>{{1,2,10,11},{3,9},{4,8},{5,7},{6}}
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[6,5,7,4,8,3,9,2,10,1]=>{{1,3,6,7,9,10},{2,5,8},{4}}
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}}
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,2,1,3]=>{{1,2,3,7,8,9},{4,6},{5}}
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[9,8,7,6,5,3,2,1,4]=>{{1,2,3,4,6,7,8,9},{5}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[9,8,7,5,4,3,2,1,6]=>{{1,2,3,6,7,8,9},{4,5}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[9,8,6,5,4,3,2,1,7]=>{{1,2,7,8,9},{3,6},{4,5}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[9,7,6,5,4,3,2,1,8]=>{{1,8,9},{2,7},{3,6},{4,5}}
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]=>{{1,3,7,9},{2,8},{4,6},{5}}
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,2,1,3]=>{{1,2,3,8,9,10},{4,7},{5,6}}
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[9,8,7,6,5,2,3,1,4]=>{{1,2,4,6,8,9},{3,7},{5}}
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,3,2,1,4]=>{{1,2,3,4,7,8,9,10},{5,6}}
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>[9,8,7,6,3,4,2,1,5]=>{{1,2,3,5,7,8,9},{4,6}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[10,9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>[9,8,7,4,5,3,2,1,6]=>{{1,2,3,6,7,8,9},{4},{5}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[10,9,8,7,5,4,3,2,1,6]=>{{1,2,3,4,6,7,8,9,10},{5}}
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[5,6,4,3,2,1,9,8,7]=>[9,8,5,6,4,3,2,1,7]=>{{1,2,7,8,9},{3,4,5,6}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[10,9,8,6,5,4,3,2,1,7]=>{{1,2,3,7,8,9,10},{4,6},{5}}
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>[9,6,7,5,4,3,2,1,8]=>{{1,8,9},{2,3,6,7},{4,5}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[10,9,7,6,5,4,3,2,1,8]=>{{1,2,8,9,10},{3,7},{4,6},{5}}
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[10,8,7,6,5,4,3,2,1,9]=>{{1,9,10},{2,8},{3,7},{4,6},{5}}
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>{{1,7},{2,6},{3,5},{4},{8},{9}}
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>{{1,6},{2,5},{3,4},{7},{8},{9}}
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>{{1,5},{2,4},{3},{6},{7},{8},{9}}
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}}
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>{{1,8},{2,7},{3,6},{4,5},{9},{10}}
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>{{1,7},{2,6},{3,5},{4},{8},{9},{10}}
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10}}
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>{{1,5},{2,4},{3},{6},{7},{8},{9},{10}}
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>{{1,4},{2,3},{5},{6},{7},{8},{9},{10}}
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>{{1,9},{2,8},{3,7},{4,5,6}}
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>[9,8,7,6,5,3,4,2,1]=>{{1,9},{2,8},{3,4,6,7},{5}}
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,2,3,1]=>{{1,9},{2,3,7,8},{4,6},{5}}
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,5,6,7}}
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,8,1]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>[8,2,1,3,4,5,6,7,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[2,1,3,4,5,6,8,9,7]=>[8,2,1,3,4,5,6,9,7]=>{{1,3,4,5,6,7,8,9},{2}}
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>[8,6,5,4,3,2,1,7,9]=>{{1,7,8},{2,6},{3,5},{4},{9}}
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[3,4,5,6,7,8,2,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>{{1,4},{2},{3},{5},{6},{7},{8},{9}}
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[2,3,5,4,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[2,3,4,6,5,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>{{1,6},{2},{3},{4},{5},{7},{8},{9}}
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[2,3,4,5,7,6,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[8,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[9,7,6,5,4,3,2,8,1]=>{{1,9},{2,7},{3,6},{4,5},{8}}
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>[4,3,2,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2,3}}
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[5,4,3,2,6,7,8,9,1]=>[5,4,3,2,6,7,8,9,1]=>{{1,5,6,7,8,9},{2,4},{3}}
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[6,5,4,3,2,7,8,9,1]=>{{1,6,7,8,9},{2,5},{3,4}}
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>[7,6,5,4,3,2,8,9,1]=>{{1,7,8,9},{2,6},{3,5},{4}}
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,10,1]=>[4,3,2,5,6,7,8,9,10,1]=>{{1,4,5,6,7,8,9,10},{2,3}}
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[5,4,3,2,6,7,8,9,10,1]=>[5,4,3,2,6,7,8,9,10,1]=>{{1,5,6,7,8,9,10},{2,4},{3}}
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[6,5,4,3,2,7,8,9,10,1]=>[6,5,4,3,2,7,8,9,10,1]=>{{1,6,7,8,9,10},{2,5},{3,4}}
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[7,6,5,4,3,2,8,9,10,1]=>[7,6,5,4,3,2,8,9,10,1]=>{{1,7,8,9,10},{2,6},{3,5},{4}}
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1]=>[8,7,6,5,4,3,2,9,10,1]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]=>{{1,2,7,8,9},{3,6},{4,5}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[8,6,5,4,3,2,1,9,7]=>{{1,7,8,9},{2,6},{3,5},{4}}
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]=>{{1,3,8,10},{2,9},{4,7},{5,6}}
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]=>{{1,3,4,6,7,9},{2,8},{5}}
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[8,7,6,5,4,2,1,3,9]=>{{1,2,3,6,7,8},{4,5},{9}}
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[9,8,7,6,5,4,3,1,2,10]=>{{1,2,8,9},{3,7},{4,6},{5},{10}}
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>[4,1,2,5,3,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>[4,2,1,5,3,6,7,8,9]=>{{1,3,4,5},{2},{6},{7},{8},{9}}
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>{{1,10},{2,8},{3,7},{4,6},{5},{9}}
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[3,1,4,5,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[6,7,8,5,4,3,2,1,9]=>{{1,3,6,8},{2,7},{4,5},{9}}
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[6,5,7,8,4,3,2,1,9]=>[6,5,7,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.]=>[6,5,4,7,8,3,2,1,9]=>[6,5,4,7,8,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.]=>[6,5,4,3,7,8,2,1,9]=>[6,5,4,3,7,8,2,1,9]=>{{1,6,8},{2,5,7},{3,4},{9}}
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>[6,5,4,3,2,7,8,1,9]=>{{1,6,7,8},{2,5},{3,4},{9}}
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[7,8,9,6,5,4,3,2,1,10]=>{{1,3,7,9},{2,8},{4,6},{5},{10}}
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[7,6,8,9,5,4,3,2,1,10]=>[7,6,8,9,5,4,3,2,1,10]=>{{1,2,3,4,6,7,8,9},{5},{10}}
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[7,6,5,8,9,4,3,2,1,10]=>[7,6,5,8,9,4,3,2,1,10]=>{{1,3,5,7,9},{2,4,6,8},{10}}
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.]=>[7,6,5,4,8,9,3,2,1,10]=>[7,6,5,4,8,9,3,2,1,10]=>{{1,2,3,5,6,7,8,9},{4},{10}}
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[7,6,5,4,3,8,9,2,1,10]=>[7,6,5,4,3,8,9,2,1,10]=>{{1,7,9},{2,6,8},{3,5},{4},{10}}
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[7,6,5,4,3,2,8,9,1,10]=>[7,6,5,4,3,2,8,9,1,10]=>{{1,7,8,9},{2,6},{3,5},{4},{10}}
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]=>{{1,3,4,6,7,9},{2,5,8}}
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>{{1,5,9},{2,4,6,8},{3,7}}
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]=>{{1,4,6,9},{2,3,7,8},{5}}
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]=>{{1,4,7,10},{2,3,5,6,8,9}}
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]=>{{1,2,5,6,9,10},{3,4,7,8}}
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]=>{{1,5,6,10},{2,4,7,9},{3,8}}
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,1,2,3,4]=>{{1,4,7,10},{2,3,8,9},{5,6}}
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[10,9,11,8,7,6,5,4,3,2,1]=>{{1,2,3,9,10,11},{4,8},{5,7},{6}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[10,11,9,8,7,6,5,4,3,2,1]=>{{1,2,10,11},{3,9},{4,8},{5,7},{6}}
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[7,8,6,5,4,3,2,9,1]=>{{1,2,7,8,9},{3,6},{4,5}}
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10,11]=>[2,3,1,4,5,6,7,8,9,10,11]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>[3,4,2,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10,11]=>[3,1,2,4,5,6,7,8,9,10,11]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[7,6,5,4,3,2,8,1,9]=>{{1,7,8},{2,6},{3,5},{4},{9}}
[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]=>[5,8,7,6,4,3,2,1,9]=>[8,7,5,6,4,3,2,1,9]=>{{1,8},{2,7},{3,4,5,6},{9}}
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[6,5,8,7,4,3,2,1,9]=>[8,6,5,7,4,3,2,1,9]=>{{1,8},{2,3,4,5,6,7},{9}}
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[7,6,5,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]=>[7,6,10,9,8,5,4,3,2,1]=>[10,9,7,6,8,5,4,3,2,1]=>{{1,10},{2,9},{3,4,5,6,7,8}}
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[6,7,5,8,4,3,2,1,9]=>[6,7,5,8,4,3,2,1,9]=>{{1,3,4,5,6,8},{2,7},{9}}
[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]=>[4,9,8,7,6,5,3,2,1,10]=>[9,8,7,6,4,5,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,5,6},{10}}
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>{{1,2,4,5},{3},{6},{7},{8},{9}}
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[3,2,4,5,6,7,8,1,9]=>{{1,3,4,5,6,7,8},{2},{9}}
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>[8,7,5,4,3,2,1,6,9]=>{{1,2,6,7,8},{3,5},{4},{9}}
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>[9,7,6,5,4,3,2,1,8,10]=>{{1,8,9},{2,7},{3,6},{4,5},{10}}
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[9,8,7,6,5,2,3,4,1]=>{{1,9},{2,4,6,8},{3,7},{5}}
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[8,7,6,5,4,2,3,1,9]=>{{1,8},{2,3,6,7},{4,5},{9}}
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[9,2,3,4,5,6,7,1,8]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[8,7,6,5,4,3,2,9,1,10]=>{{1,8,9},{2,7},{3,6},{4,5},{10}}
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]=>[8,7,6,5,4,1,2,3,9]=>{{1,3,6,8},{2,7},{4,5},{9}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}
[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[1,3,2,4,5,6,8,7,9]=>[8,3,1,2,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>{{1,2,5,6},{3,4},{7},{8},{9}}
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[5,6,4,3,2,1,7,8,9,10]=>{{1,2,5,6},{3,4},{7},{8},{9},{10}}
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[6,7,5,4,3,2,1,8,9,10,11]=>{{1,2,6,7},{3,5},{4},{8},{9},{10},{11}}
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[6,7,5,4,3,2,1,8,9,10]=>{{1,2,6,7},{3,5},{4},{8},{9},{10}}
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[5,6,4,3,2,7,1,8,9]=>{{1,2,5,6,7},{3,4},{8},{9}}
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,8,10,9]=>[10,3,1,2,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[6,7,5,4,3,2,1,8,9]=>{{1,2,6,7},{3,5},{4},{8},{9}}
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[5,4,3,2,1,8,9,7,6]=>[8,9,5,4,3,2,1,7,6]=>{{1,7,8},{2,6,9},{3,5},{4}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>[9,7,6,5,4,3,2,1,10,8]=>{{1,8,9,10},{2,7},{3,6},{4,5}}
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
searching the database
Sorry, this map was not found in the database.