Identifier
Mp00017:
Binary trees
—to 312-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]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[[.,[.,.]],.]=>[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]=>[[.,[[.,.],.]],.]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[[[.,[.,.]],.],.]=>[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]=>[[.,[.,[[.,.],.]]],.]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[[[[.,[.,.]],.],.],.]=>[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]=>[[.,[.,[.,[[.,.],.]]]],.]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[[.,[[.,.],[[.,.],.]]],.]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[[[.,.],[[[.,.],.],.]],.]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[[[.,.],[[.,[.,.]],.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[.,[[[[.,.],[.,.]],.],.]]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[[[[[[.,[.,.]],.],.],.],.],.]=>[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]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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
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 maximima 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 deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of 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.