Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[2,3,1]
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[3,1,2]
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[3,2,1]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>[3,1,4,2]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,2,3,1]=>[3,4,2,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>[2,4,1,3]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,4,2,1]=>[2,4,3,1]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,4,1,2]=>[4,1,3,2]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,2,4,1]=>[4,3,2,1]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[4,2,3,1]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[3,1,2,4]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[3,2,1,4]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[3,1,4,5,2]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[3,4,2,5,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[2,4,1,5,3]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[4,1,2,5,3]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[2,4,5,3,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[4,1,5,3,2]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[4,3,5,2,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[4,5,2,3,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[2,3,5,1,4]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[3,1,5,2,4]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,2,3,1,4]=>[3,5,2,1,4]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[2,5,1,3,4]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[2,3,5,4,1]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[3,1,5,4,2]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,5,2,3,1]=>[3,5,2,4,1]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,5,2,1,3]=>[2,5,1,4,3]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[4,5,1,2,3]=>[5,1,2,4,3]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[2,5,4,3,1]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,3,5,1,2]=>[5,1,4,3,2]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[2,5,3,4,1]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,4,5,1,2]=>[5,1,3,4,2]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[5,3,4,2,1]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,2,3,5,1]=>[5,4,2,3,1]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,4,3,2,1]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[5,3,2,4,1]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,2,3,4,1]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[3,1,4,2,5]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,1,3,5]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[4,1,2,3,5]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[2,4,3,1,5]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[4,1,3,2,5]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[4,3,2,1,5]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[4,2,3,1,5]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[2,5,4,6,3,7,8,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[8,7,6,3,4,5,1,2]=>[5,1,6,3,4,7,8,2]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[5,3,4,6,2,7,8,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[5,4,6,3,2,7,8,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[5,6,2,3,4,7,8,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[3,4,2,6,1,7,8,5]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[2,4,6,3,1,7,8,5]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[4,3,6,2,1,7,8,5]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[4,6,2,3,1,7,8,5]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[3,1,4,6,7,5,8,2]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[2,3,6,5,7,4,8,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[3,6,2,5,7,4,8,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,5,4,6,1,2,3]=>[6,1,2,5,7,4,8,3]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[8,7,4,5,6,2,3,1]=>[3,6,2,7,4,5,8,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[8,7,4,5,6,2,1,3]=>[2,6,1,7,4,5,8,3]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[2,6,4,5,7,3,8,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[8,7,4,5,3,6,1,2]=>[6,1,5,7,4,3,8,2]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[8,7,4,3,5,6,1,2]=>[6,1,4,7,3,5,8,2]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,3,4,5,6,2,1]=>[2,6,7,3,4,5,8,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[6,3,5,2,7,4,8,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[8,7,4,5,1,2,3,6]=>[5,1,2,7,4,3,8,6]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[2,5,7,3,4,1,8,6]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,2,5,1,6]=>[5,3,4,7,2,1,8,6]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>[5,4,7,3,2,1,8,6]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>[4,3,7,2,1,5,8,6]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[2,3,4,5,7,8,6,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[3,4,2,5,7,8,6,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[4,3,5,2,7,8,6,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[8,6,7,5,2,3,4,1]=>[4,5,2,3,7,8,6,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[2,3,5,1,7,8,6,4]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[2,3,5,7,4,8,6,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,3]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[5,3,4,7,2,8,6,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[2,3,4,7,1,8,6,5]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[2,3,4,7,6,8,5,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[8,6,5,7,2,3,4,1]=>[4,7,2,3,6,8,5,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[8,6,5,7,2,3,1,4]=>[3,7,2,1,6,8,5,4]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,5,6,7,4,2,3,1]=>[3,4,2,7,8,5,6,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,5,6,7,3,4,2,1]=>[2,4,7,3,8,5,6,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[8,5,6,7,2,1,3,4]=>[2,7,1,3,8,5,6,4]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[3,7,2,5,6,8,4,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[8,6,5,4,7,1,2,3]=>[7,1,2,5,6,8,4,3]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[2,3,7,6,4,8,5,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[3,7,2,6,4,8,5,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,6,4,5,7,1,2,3]=>[7,1,2,6,4,8,5,3]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[8,5,6,4,7,3,2,1]=>[2,3,7,6,8,5,4,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[8,5,6,4,7,3,1,2]=>[3,1,7,6,8,5,4,2]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,4,3,6,7,1,2]=>[7,1,4,5,8,3,6,2]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,6,3,4,5,2,7,1]=>[7,5,6,3,4,8,2,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[7,4,2,6,3,8,5,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[2,4,5,3,6,8,1,7]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[4,3,5,2,6,8,1,7]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,2,3,4,1,7]=>[4,5,2,3,6,8,1,7]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[3,1,5,6,4,8,2,7]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[6,7,3,4,5,2,8,1]=>[8,6,3,4,5,1,2,7]=>[5,1,6,3,4,8,2,7]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[5,4,2,6,3,8,1,7]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[3,4,2,6,1,8,5,7]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,3,4,1,2,5,7]=>[4,1,6,3,2,8,5,7]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,5,6,4,3,2,1,7]=>[2,3,4,6,8,5,1,7]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,5,6,4,2,3,1,7]=>[3,4,2,6,8,5,1,7]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,5,6,2,3,4,1,7]=>[4,6,2,3,8,5,1,7]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,5,6,3,1,2,4,7]=>[3,1,6,2,8,5,4,7]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,5,6,2,1,3,4,7]=>[2,6,1,3,8,5,4,7]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,4,5,6,1,2,3,7]=>[6,1,2,8,4,5,3,7]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,5,3,6,2,1,7]=>[2,6,5,8,4,3,1,7]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[8,4,5,3,6,1,2,7]=>[6,1,5,8,4,3,2,7]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,3,5,6,1,2,7]=>[6,1,4,8,3,5,2,7]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[8,3,4,5,6,2,1,7]=>[2,6,8,3,4,5,1,7]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,3,4,5,6,1,2,7]=>[6,1,8,3,4,5,2,7]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,2,3,4,6,1,7]=>[6,5,2,3,8,4,1,7]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,4,5,3,2,1,6,7]=>[2,3,5,8,4,1,6,7]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[8,4,5,2,3,1,6,7]=>[3,5,2,8,4,1,6,7]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[6,3,4,2,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[7,8,6,5,3,4,2,1]=>[2,4,5,3,6,8,7,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[7,8,6,5,3,2,4,1]=>[4,3,5,2,6,8,7,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[7,8,6,5,3,2,1,4]=>[2,3,5,1,6,8,7,4]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[7,8,6,5,3,1,2,4]=>[3,1,5,2,6,8,7,4]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[7,8,6,4,3,5,2,1]=>[2,5,4,6,3,8,7,1]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[7,8,6,3,4,5,2,1]=>[2,5,6,3,4,8,7,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[7,8,6,3,4,5,1,2]=>[5,1,6,3,4,8,7,2]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,3,1,2]=>[7,8,6,4,3,2,5,1]=>[5,3,4,6,2,8,7,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[7,8,6,4,2,1,3,5]=>[2,4,1,6,3,8,7,5]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[7,8,6,3,4,2,1,5]=>[2,4,6,3,1,8,7,5]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[7,8,6,2,1,3,4,5]=>[2,6,1,3,4,8,7,5]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[7,8,5,6,2,3,4,1]=>[4,6,2,3,8,5,7,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,8,5,6,2,3,1,4]=>[3,6,2,1,8,5,7,4]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,8,4,5,3,6,1,2]=>[6,1,5,8,4,3,7,2]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,3,7,1,2]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,8,4,3,5,2,6,1]=>[6,5,4,8,3,2,7,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,8,3,4,2,5,6,1]=>[6,4,8,3,2,5,7,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[7,8,4,5,2,3,1,6]=>[3,5,2,8,4,1,7,6]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[7,8,3,4,5,2,1,6]=>[2,5,8,3,4,1,7,6]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[7,8,4,3,2,5,1,6]=>[5,3,4,8,2,1,7,6]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[7,8,4,2,3,1,5,6]=>[3,4,2,8,1,5,7,6]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[7,8,4,1,2,3,5,6]=>[4,1,2,8,3,5,7,6]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[7,8,3,4,1,2,5,6]=>[4,1,8,3,2,5,7,6]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[7,6,8,5,4,2,3,1]=>[3,4,2,5,8,7,6,1]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[7,6,8,5,2,3,4,1]=>[4,5,2,3,8,7,6,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[7,6,8,5,2,1,3,4]=>[2,5,1,3,8,7,6,4]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[7,6,8,4,5,3,2,1]=>[2,3,5,8,4,7,6,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[7,6,8,3,4,5,2,1]=>[2,5,8,3,4,7,6,1]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,2,1,3]=>[7,6,8,4,2,3,5,1]=>[5,4,2,8,3,7,6,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[7,6,8,4,2,3,1,5]=>[3,4,2,8,1,7,6,5]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[7,6,8,4,1,2,3,5]=>[4,1,2,8,3,7,6,5]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[7,6,8,3,2,1,4,5]=>[2,3,8,1,4,7,6,5]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[7,6,8,2,3,1,4,5]=>[3,8,2,1,4,7,6,5]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[6,7,8,5,4,2,1,3]=>[2,4,1,5,8,6,7,3]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[6,7,8,5,3,4,1,2]=>[4,1,5,3,8,6,7,2]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[6,7,8,5,3,2,1,4]=>[2,3,5,1,8,6,7,4]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[6,7,8,5,2,3,1,4]=>[3,5,2,1,8,6,7,4]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[6,7,8,4,2,1,3,5]=>[2,4,1,8,3,6,7,5]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[6,7,8,3,4,2,1,5]=>[2,4,8,3,1,6,7,5]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[6,7,8,2,3,4,1,5]=>[4,8,2,3,1,6,7,5]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[6,7,8,3,1,2,4,5]=>[3,1,8,2,4,6,7,5]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,6,5,8,4,3,1,2]=>[3,1,4,8,6,7,5,2]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[7,6,5,8,4,1,2,3]=>[4,1,2,8,6,7,5,3]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[7,6,5,8,3,4,2,1]=>[2,4,8,3,6,7,5,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[7,6,5,8,2,3,4,1]=>[4,8,2,3,6,7,5,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[7,5,6,8,4,3,1,2]=>[3,1,4,8,7,5,6,2]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[7,5,6,8,4,2,3,1]=>[3,4,2,8,7,5,6,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[7,5,6,8,4,2,1,3]=>[2,4,1,8,7,5,6,3]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[7,5,6,8,3,2,1,4]=>[2,3,8,1,7,5,6,4]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[6,7,5,8,3,4,1,2]=>[4,1,8,3,7,6,5,2]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[6,7,5,8,2,3,4,1]=>[4,8,2,3,7,6,5,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[6,5,7,8,4,2,1,3]=>[2,4,1,8,6,5,7,3]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,5,7,8,4,1,2,3]=>[4,1,2,8,6,5,7,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[6,5,7,8,2,3,4,1]=>[4,8,2,3,6,5,7,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[6,5,7,8,2,3,1,4]=>[3,8,2,1,6,5,7,4]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,4,5,8,3,2,1]=>[2,3,8,6,4,7,5,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[7,6,8,3,4,2,1,5]=>[7,6,4,5,8,2,1,3]=>[2,8,1,6,4,7,5,3]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[7,5,6,4,8,2,1,3]=>[2,8,1,6,7,5,4,3]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,5,4,6,8,3,2,1]=>[2,3,8,5,7,4,6,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[6,7,5,4,8,2,1,3]=>[2,8,1,5,7,6,4,3]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,7,5,4,8,1,2,3]=>[8,1,2,5,7,6,4,3]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[6,7,4,5,8,3,2,1]=>[2,3,8,7,4,6,5,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[6,7,4,5,8,3,1,2]=>[3,1,8,7,4,6,5,2]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[2,3,8,7,5,6,4,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,6,7,4,8,1,2,3]=>[8,1,2,7,5,6,4,3]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,5,4,7,8,1,2,3]=>[8,1,2,5,6,4,7,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[5,6,4,7,8,3,1,2]=>[3,1,8,6,5,4,7,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,6,4,7,8,1,2,3]=>[8,1,2,6,5,4,7,3]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,6,7,8,1,2,3]=>[8,1,2,5,4,6,7,3]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[7,6,3,4,5,8,2,1]=>[2,8,6,3,4,7,5,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[7,6,3,4,5,8,1,2]=>[8,1,6,3,4,7,5,2]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[7,5,6,4,3,8,2,1]=>[2,8,4,6,7,5,3,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[7,5,4,6,3,8,1,2]=>[8,1,6,5,7,4,3,2]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[7,4,5,6,3,8,2,1]=>[2,8,6,7,4,5,3,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[7,5,4,3,6,8,2,1]=>[2,8,4,5,7,3,6,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[7,5,3,4,6,8,2,1]=>[2,8,5,3,7,4,6,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[7,4,5,3,6,8,1,2]=>[8,1,5,7,4,3,6,2]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[5,6,7,4,3,8,1,2]=>[8,1,4,7,5,6,3,2]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[5,4,6,7,3,8,1,2]=>[8,1,7,5,4,6,3,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,8,1,2]=>[8,1,7,4,5,6,3,2]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,8,1,2]=>[8,1,6,5,4,3,7,2]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[4,5,6,3,7,8,1,2]=>[8,1,6,4,5,3,7,2]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[5,3,4,6,7,8,1,2]=>[8,1,5,3,4,6,7,2]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,4,5,6,3,2,8,1]=>[8,3,6,7,4,5,2,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,3,1,2,7]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[6,7,5,3,2,4,8,1]=>[8,3,5,2,7,6,4,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[6,7,3,2,4,5,8,1]=>[8,3,7,2,4,6,5,1]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[6,7,2,3,4,5,8,1]=>[8,7,2,3,4,6,5,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[6,5,7,4,2,3,8,1]=>[8,4,2,7,6,5,3,1]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[5,6,7,4,2,3,8,1]=>[8,4,2,7,5,6,3,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[5,6,7,2,3,4,8,1]=>[8,7,2,3,5,6,4,1]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,4,5,7,3,2,8,1]=>[8,3,7,6,4,5,2,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[5,6,4,7,2,3,8,1]=>[8,7,2,6,5,4,3,1]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,4,6,7,2,3,8,1]=>[8,7,2,5,4,6,3,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[6,5,4,2,3,7,8,1]=>[8,4,2,5,6,3,7,1]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,5,2,3,4,7,8,1]=>[8,5,2,3,6,4,7,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,4,5,2,3,7,8,1]=>[8,5,2,6,4,3,7,1]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[8,4,5,3,1,2,6,7]=>[5,6,4,2,3,7,8,1]=>[8,4,2,6,5,3,7,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[5,4,6,2,3,7,8,1]=>[8,6,2,5,4,3,7,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[5,4,2,3,6,7,8,1]=>[8,4,2,5,3,6,7,1]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[8,5,2,3,4,6,7,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,5,2,3,6,7,8,1]=>[8,5,2,4,3,6,7,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>[2,4,5,3,6,7,1,8]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>[3,5,2,1,6,7,4,8]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[2,5,1,3,6,7,4,8]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[7,6,4,5,3,2,1,8]=>[2,3,5,6,4,7,1,8]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[7,6,4,5,1,2,3,8]=>[5,1,2,6,4,7,3,8]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[2,5,6,3,4,7,1,8]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,2,3,4,5,1,8]=>[5,6,2,3,4,7,1,8]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[7,6,2,3,4,1,5,8]=>[4,6,2,3,1,7,5,8]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[2,3,6,1,4,7,5,8]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[5,3,4,6,7,2,1,8]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,5,6,4,3,2,1,8]=>[2,3,4,6,7,5,1,8]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,5,6,4,2,3,1,8]=>[3,4,2,6,7,5,1,8]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,5,6,3,1,2,4,8]=>[3,1,6,2,7,5,4,8]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[7,5,6,2,3,1,4,8]=>[3,6,2,1,7,5,4,8]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,5,4,6,1,2,3,8]=>[6,1,2,5,7,4,3,8]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,4,5,6,3,2,1,8]=>[2,3,6,7,4,5,1,8]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,4,5,6,3,1,2,8]=>[3,1,6,7,4,5,2,8]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,4,5,6,2,3,1,8]=>[3,6,2,7,4,5,1,8]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,4,5,6,2,1,3,8]=>[2,6,1,7,4,5,3,8]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,4,5,6,1,2,3,8]=>[6,1,2,7,4,5,3,8]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[7,5,3,4,6,1,2,8]=>[6,1,5,3,7,4,2,8]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,4,5,3,6,2,1,8]=>[2,6,5,7,4,3,1,8]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,5,3,4,2,6,1,8]=>[6,4,5,3,7,2,1,8]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[7,4,5,3,2,6,1,8]=>[6,3,5,7,4,2,1,8]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1,8]=>[6,5,2,7,4,3,1,8]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,3,4,1,2,6,8]=>[4,1,5,3,7,2,6,8]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[2,3,5,1,7,4,6,8]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[5,1,2,3,7,4,6,8]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,4,5,1,2,3,6,8]=>[5,1,2,7,4,3,6,8]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[6,3,4,2,5,7,1,8]=>[7,4,2,3,5,1,6,8]=>[5,4,2,7,3,1,6,8]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,4,3,1,2,5,6,8]=>[3,1,4,7,2,5,6,8]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,3,1,2,8]=>[6,7,5,3,4,2,1,8]=>[2,4,5,3,7,6,1,8]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,3,1,2,8]=>[6,7,5,2,3,1,4,8]=>[3,5,2,1,7,6,4,8]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[6,7,3,4,5,1,2,8]=>[5,1,7,3,4,6,2,8]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[6,7,4,3,2,5,1,8]=>[5,3,4,7,2,6,1,8]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[6,7,3,4,2,5,1,8]=>[5,4,7,3,2,6,1,8]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[6,7,3,2,4,5,1,8]=>[5,3,7,2,4,6,1,8]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[6,7,2,3,4,1,5,8]=>[4,7,2,3,1,6,5,8]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[6,7,3,2,1,4,5,8]=>[2,3,7,1,4,6,5,8]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[6,7,3,1,2,4,5,8]=>[3,1,7,2,4,6,5,8]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[6,5,7,3,4,2,1,8]=>[2,4,7,3,6,5,1,8]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[6,5,7,3,4,1,2,8]=>[4,1,7,3,6,5,2,8]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[5,4,6,7,3,1,2,8]=>[3,1,7,5,4,6,2,8]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[5,4,6,7,2,3,1,8]=>[3,7,2,5,4,6,1,8]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[2,3,7,4,5,6,1,8]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[4,5,6,7,2,3,1,8]=>[3,7,2,4,5,6,1,8]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[4,5,6,7,2,1,3,8]=>[2,7,1,4,5,6,3,8]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[6,5,4,3,7,1,2,8]=>[7,1,4,5,6,3,2,8]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[6,4,5,3,7,1,2,8]=>[7,1,5,6,4,3,2,8]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[2,7,4,5,3,6,1,8]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[6,3,2,4,5,7,1,8]=>[7,3,6,2,4,5,1,8]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[7,3,4,5,2,6,1,8]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,5,2,3,6,7,1,8]=>[7,5,2,4,3,6,1,8]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[3,1,4,5,6,2,7,8]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[2,4,5,3,6,1,7,8]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[6,5,2,3,4,1,7,8]=>[4,5,2,3,6,1,7,8]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,3,5,1,2,7,8]=>[5,1,4,6,3,2,7,8]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[5,3,4,6,2,1,7,8]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[3,1,4,6,2,5,7,8]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,3,4,2,1,5,7,8]=>[2,4,6,3,1,5,7,8]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[6,3,4,5,2,1,7,8]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[5,3,2,4,6,1,7,8]=>[6,3,5,2,4,1,7,8]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[6,3,5,4,2,1,7,8]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>[4,1,5,3,2,6,7,8]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[3,1,5,2,4,6,7,8]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
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
inverse
Description
Sends a permutation to its inverse.
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
searching the database
Sorry, this map was not found in the database.