Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ 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]=>[3,1,2]=>[[.,.],[.,.]]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[[.,[.,.]],.]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[.,[[[.,[.,.]],.],.]]=>[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]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[[.,[[.,[.,.]],.]],.]=>[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]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[[.,[.,.]],.],.],.]=>[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]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,1,4,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,1,4,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,1,5,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,1,4,5,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,3,1,2,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,3,1,5,4,2]=>[[[.,.],.],[[[.,.],.],.]]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,3,1,4,5,2]=>[[[.,.],.],[[.,[.,.]],.]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,2,1,5,3]=>[[[[.,.],.],.],[[.,.],.]]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[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]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[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]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,6,1,5,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,6,1,5,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,6,1,4,5,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>[[.,[[.,.],.]],[.,[.,.]]]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>[[.,[[[.,.],.],.]],[.,.]]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,6,4,5,1,3]=>[[.,[[.,.],[.,.]]],[.,.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,6,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,6,5,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>[[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,6,4,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,3,6,1,5,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>[[.,[.,[[.,.],.]]],[.,.]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,3,1,6,2,5]=>[[[.,.],.],[[.,.],[.,.]]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,3,1,6,5,2]=>[[[.,.],.],[[[.,.],.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,4,1,6,5,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,1,4,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,4,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,4,2,1,6,3]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,3,4,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>[[.,[[.,.],.]],[[.,.],.]]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,1,4,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,5,1,4,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,1,5,4,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[[[[.,[.,.]],.],.],.],.]=>[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]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,1,2,3,6,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,1,2,5,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,1,2,5,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,1,2,6,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,1,2,5,6,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,1,4,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,1,4,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,1,4,2,6,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,1,4,2,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,1,4,2,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,1,5,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,1,5,3,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,1,4,5,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,1,4,5,2,6,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,1,6,3,4,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,1,6,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,1,4,6,3,2,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,1,5,3,6,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,1,4,5,6,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,1,6,5,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,1,4,6,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,1,4,6,5,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,1,5,3,6,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,1,4,5,6,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,1,4,5,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,3,1,2,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,3,1,2,6,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,3,1,2,6,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,3,1,2,5,6,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,3,1,5,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,3,1,5,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,3,1,6,4,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,3,1,5,6,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,3,1,6,4,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,3,1,6,5,4,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,3,1,5,6,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,3,1,5,4,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,3,1,4,5,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,4,2,1,3,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,4,2,1,6,3,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,4,2,1,6,5,3]=>[[[[.,.],.],.],[[[.,.],.],.]]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,4,2,1,5,6,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,3,4,1,2,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,3,4,1,6,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,3,4,1,6,5,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,3,4,1,5,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,2,3,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,4,2,1,6,3]=>[[[[[.,.],.],.],.],[[.,.],.]]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,3,5,2,1,4,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,3,5,2,1,6,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,2,5,1,6,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,6,2,5,3,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,6,4,5,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,3,6,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,3,6,5,2,1,4]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,2,6,3,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,6,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,5,2,3,6,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,5,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,4,2,5,6,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,6,2,5,3,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,6,4,2,5,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,6,4,5,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[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]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,3,6,2,5,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,3,6,5,2,4,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,2,6,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,2,6,5,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,5,2,3,6,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,5,4,2,6,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,5,2,6,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,4,2,5,6,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[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]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,5,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,5,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,4,2,5,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[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]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,7,1,3,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,7,1,3,6,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,7,1,3,6,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,7,1,3,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,7,1,5,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,7,1,5,3,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,7,1,6,4,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,7,1,5,6,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,7,1,6,4,5,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,7,1,6,5,4,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,7,1,5,6,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,7,1,5,4,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,7,1,4,5,6,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,7,4,1,3,6,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,7,4,1,5,6,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,7,5,3,1,6,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,7,4,5,1,3,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,7,4,5,1,6,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,7,6,5,3,1,4]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,7,4,6,3,1,5]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,7,5,3,6,1,4]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,7,4,5,6,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,7,6,3,5,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,7,6,5,3,4,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,7,4,6,3,5,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,7,5,3,6,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,7,5,3,4,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,7,5,4,3,6,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,7,4,5,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,7,4,3,5,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,7,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,7,2,6,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,7,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,7,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,7,5,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,7,5,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,7,6,4,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,7,5,6,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,7,6,4,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,7,6,5,4,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,7,5,6,4,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,7,5,4,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,7,4,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,3,7,1,4,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[2,3,7,1,6,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[2,3,7,1,6,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[2,3,7,1,5,6,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,7,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,7,6,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,7,6,5,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,7,5,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,3,1,7,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,3,1,7,2,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,3,1,7,6,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,3,1,7,6,5,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,3,1,7,5,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,4,1,7,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[2,4,1,7,6,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[2,4,1,7,6,5,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[2,4,1,7,5,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[3,1,4,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[3,1,4,7,6,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[3,1,4,7,6,5,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,4,7,5,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,3,4,7,1,6,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,4,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,4,2,7,6,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,3,1,2,7,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,3,1,2,7,6,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,4,2,1,7,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,4,2,1,7,6,3]=>[[[[.,.],.],.],[[[.,.],.],.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,3,4,1,7,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,3,4,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,5,1,3,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[3,1,5,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,3,5,1,7,6,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,3,1,5,7,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[4,3,1,5,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,4,1,5,7,6,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[3,1,4,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,5,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,4,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,5,3,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,4,5,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,3,1,5,2,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,2,1,3,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,1,2,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,5,2,3,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,5,4,2,1,7,3]=>[[[[[.,.],.],.],.],[[.,.],.]]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,5,2,1,7,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,4,2,5,1,7,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,3,4,5,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[2,6,1,5,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[2,6,4,5,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[3,1,6,5,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[4,3,1,6,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,1,4,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,1,2,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,4,2,1,6,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,3,4,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,1,2,5,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,1,4,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,1,4,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,1,5,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,1,4,5,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,1,4,5,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,3,1,2,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,3,1,5,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,3,1,5,4,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,3,1,4,5,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,2,1,5,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,1,5,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,5,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,3,4,5,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[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]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,5,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,4,2,5,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[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]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,6,1,3,5,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[2,6,1,5,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[2,6,1,5,4,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[2,6,1,4,5,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[2,6,4,5,1,3,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[2,6,4,5,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[2,6,4,3,5,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,1,6,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[3,1,6,5,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,1,6,5,4,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,6,4,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,3,6,1,5,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[4,3,1,6,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[4,3,1,6,5,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,4,1,6,5,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,1,4,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,1,4,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,4,2,1,6,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,3,4,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,1,4,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[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]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,5,1,4,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[3,1,5,4,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[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]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.