Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.]
[.,[.,.]]=>[2,1]=>[2,1]=>[[.,.],.]
[[.,.],.]=>[1,2]=>[1,2]=>[.,[.,.]]
[.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[[[.,[.,.]],[[.,.],.]],.]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[[[.,[.,.]],[[.,.],.]],.]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[[[.,[.,.]],[[.,.],.]],.]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[[.,.],[[[[.,.],.],.],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[[[.,[.,.]],.],[[.,.],.]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[[[.,[.,.]],.],[[.,.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[[.,[[.,[.,.]],.]],[.,.]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
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[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
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[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
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[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
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[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
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[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
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[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[3,8,2,5,7,4,6,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[4,3,6,2,7,5,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[4,3,6,2,8,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[5,3,4,6,2,8,7,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[5,4,6,3,2,8,7,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[5,4,8,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[5,3,6,2,4,8,7,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
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[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
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[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1]=>[6,5,8,3,4,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[6,4,2,5,8,3,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
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[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[6,4,7,3,2,5,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[6,7,2,3,4,5,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
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[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
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[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[7,6,2,5,8,4,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[7,3,5,8,4,2,6,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
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[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
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[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,3,5,6,4,7,2,1]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
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[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[8,1,5,3,6,4,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[2,4,1,7,6,8,5,3]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[2,5,1,8,4,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[2,6,1,5,8,4,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[2,7,1,5,6,8,4,3]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[2,8,1,5,6,4,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[3,1,5,2,8,7,6,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[3,1,5,2,8,6,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[2,5,1,3,7,8,6,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
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[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
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[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
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[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[5,4,2,8,3,1,7,6]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[5,1,4,8,3,2,7,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[3,7,2,1,4,5,8,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
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[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,9,1]=>[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],.]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>[[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]],.]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[8,9,2,3,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[2,3,4,6,1,5,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[2,3,4,5,7,1,6,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,9,2,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>[[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>[[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>[[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,10,2,9]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the 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 maximal element of the Sylvester class.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.