Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00064: Permutations —reverse⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0002;cc-rep-3
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[1,2]=>[1,1]
[[.,.],.]=>[1,2]=>[2,1]=>[2]
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>[1,1,1]
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>[2,1]
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>[3]
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>[3]
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>[2,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>[1,1,1,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>[2,1,1]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[1,3,4,2]=>[3,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>[3,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,3,4,1]=>[4]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,3,1]=>[3,1]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,4,2,1]=>[4]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>[4]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>[3,1]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[4,2,3,1]=>[2,1,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>[4]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>[2,2]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,1,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[2,1,1,1]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[3,1,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[3,1,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[2,1,1,1]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[4,1]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[3,1,1]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[2,2,1]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[4,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[3,1,1]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[2,1,1,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[4,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[2,2,1]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[5]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[4,1]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[5]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[3,1,1]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[3,2]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[5]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[3,2]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[5]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[5]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[3,2]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[5]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,2,1]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[4,1]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[5]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[4,1]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[3,1,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[5]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[3,2]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[2,1,1,1]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[2,2,1]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[5]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[3,2]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[3,2]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[5]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[3,2]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[4,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[2,2,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[2,1,1,1,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[3,1,1,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[3,1,1,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[2,1,1,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[4,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[3,1,1,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[2,2,1,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[4,1,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[4,1,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[3,1,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[2,1,1,1,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[4,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[2,2,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[5,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[4,1,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[5,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[3,1,1,1]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[3,2,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[5,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[3,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[3,2,1]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[5,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[5,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[3,2,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[5,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[2,2,1,1]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[4,1,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[5,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[4,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[3,1,1,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[5,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[3,2,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[2,1,1,1,1]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[5,1]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[3,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[3,2,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[5,1]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[3,2,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[4,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[2,2,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[6]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[5,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[6]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[4,1,1]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[4,2]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[4,2]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[6]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[6]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[5,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[3,1,1,1]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[3,2,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[3,3]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[3,3]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[3,2,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[3,3]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[6]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[5,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[4,2]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[3,2,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[6]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[3,3]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[3,2,1]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[6]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[5,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[2,2,2]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[4,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[4,2]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[2,2,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[6]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[4,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[6]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[4,2]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[4,2]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[6]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[3,3]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[6]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[4,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[5,1]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[3,2,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[6]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[5,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,1,1]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[4,1,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[6]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[4,2]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[6]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,2,2]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[4,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[6]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[5,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[4,1,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[6]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[4,2]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[3,1,1,1]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[3,2,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[6]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[3,3]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[4,2]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[6]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[3,3]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[5,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[3,2,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[2,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[2,2,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[3,2,1]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[3,2,1]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[2,2,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[6]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[5,1]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[4,2]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[3,2,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[6]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[4,2]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[2,2,2]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[6]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[4,2]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[6]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[3,3]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[6]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[3,2,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[5,1]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[4,2]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[3,2,1]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[4,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[2,2,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[4,2]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[6]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[4,2]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[4,2]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[2,2,2]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[3,1,1,1,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[2,1,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[4,1,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>[3,1,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[2,2,1,1,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[4,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[4,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[3,1,1,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[2,1,1,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[4,1,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[2,2,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[5,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>[4,1,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>[5,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>[3,1,1,1,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[5,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>[3,2,1,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[3,2,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>[5,1,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[5,1,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[3,2,1,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[5,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[2,2,1,1,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[5,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[4,1,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[3,1,1,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[5,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[3,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[2,1,1,1,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>[2,2,1,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[5,1,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[3,2,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[3,2,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[5,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[3,2,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[2,2,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[6,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>[5,1,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>[6,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>[4,1,1,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>[4,2,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>[4,2,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>[6,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>[6,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>[5,1,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>[3,1,1,1,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>[3,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>[3,3,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>[3,3,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>[3,2,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[3,3,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>[6,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>[5,1,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>[4,2,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>[3,2,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[6,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>[3,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>[3,2,1,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>[6,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>[5,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[2,2,2,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>[4,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[4,2,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>[2,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[6,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>[4,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[6,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>[4,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[4,2,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>[6,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[3,3,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[6,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[4,2,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[5,1,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[3,2,1,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[6,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>[5,1,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[2,2,1,1,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[4,1,1,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[6,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[4,2,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[6,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[2,2,2,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[4,2,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[6,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[5,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[4,1,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[6,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[4,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[3,1,1,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>[3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[6,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[3,3,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[4,2,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[6,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[3,3,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[5,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[3,2,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[2,1,1,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>[2,2,1,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>[3,2,1,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>[3,2,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>[2,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[6,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>[5,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[4,2,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>[3,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[6,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[4,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[6,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[4,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[6,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[3,3,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[6,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[3,2,1,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[5,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[4,2,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[3,2,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[4,1,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[2,2,1,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[4,2,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[6,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[4,2,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[4,2,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[2,2,2,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[7]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>[6,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>[7]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>[5,1,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>[5,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>[5,2]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>[7]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>[7]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>[6,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>[4,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>[4,2,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>[4,3]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>[4,3]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>[4,2,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[7]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>[4,3]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[4,2,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[7]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>[6,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>[7]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>[5,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>[5,2]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>[7]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>[7]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>[6,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>[5,1,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>[7]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>[5,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>[3,2,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>[3,3,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>[3,3,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>[3,2,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>[4,3]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>[3,3,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>[3,2,2]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>[4,3]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>[4,3]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>[3,3,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>[3,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>[4,3]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[3,2,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[7]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>[4,3]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>[3,3,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>[7]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>[6,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>[4,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>[7]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>[5,1,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>[5,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>[5,2]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>[4,2,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>[5,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>[3,2,1,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[3,2,2]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[4,3]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>[7]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>[6,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>[4,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>[3,3,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[7]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[4,3]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>[3,2,1,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[3,2,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>[7]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>[6,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[7]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[5,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[5,2]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[7]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>[5,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>[3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>[7]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>[4,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[5,2]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>[7]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>[4,3]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>[5,2]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[3,2,2]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[3,2,2]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>[5,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>[7]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>[7]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[5,2]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[7]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>[4,3]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>[7]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>[3,2,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[5,2]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>[7]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[5,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>[5,2]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[7]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[7]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>[5,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[5,2]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>[7]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[7]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>[5,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[3,2,2]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>[4,3]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[4,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[3,2,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[4,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>[7]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>[7]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[5,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[7]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[5,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[5,2]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[7]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[2,2,2,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>[4,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[4,2,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[2,2,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[6,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[4,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[6,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[4,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[4,2,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[6,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[7]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[4,3]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[7]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[3,3,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[6,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[5,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>[4,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[5,1,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[3,2,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[4,3]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[7]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[5,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[5,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[3,2,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[7]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>[6,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>[5,1,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>[7]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[5,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,2,1,1,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[2,2,2,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[4,1,1,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[4,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[7]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[5,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[7]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[3,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[4,3]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[7]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[4,3]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[3,2,2]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[7]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[5,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[5,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[7]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[3,2,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[4,3]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[6,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[4,2,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[6,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,2,2,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[4,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[7]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[6,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[5,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[7]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[5,2]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[4,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>[4,2,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[7]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[4,3]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[5,2]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[7]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[4,3]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[6,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[4,2,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[3,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>[3,2,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>[3,3,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>[3,3,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>[3,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[7]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>[6,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[4,3]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>[3,3,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[7]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[5,2]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[3,2,2]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[7]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[4,3]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[7]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[4,3]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[7]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[4,2,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[6,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[4,3]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>[3,3,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[5,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[3,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[5,2]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[7]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[4,3]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[5,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[3,2,2]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[2,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>[2,2,1,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>[3,2,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>[3,2,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>[2,2,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>[4,2,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[3,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>[2,2,2,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>[4,2,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>[4,2,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>[3,2,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>[2,2,1,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>[4,2,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[2,2,2,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[7]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>[6,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>[7]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>[5,1,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[5,2]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[5,2]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>[4,2,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>[5,2]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>[3,2,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[3,2,2]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[4,3]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>[7]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[7]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[5,2]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[5,2]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[3,2,2]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[5,2]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[7]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[3,2,2]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[5,2]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[3,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[5,2]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[7]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[7]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[5,2]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[5,2]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[3,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[7]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[5,2]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[6,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[4,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[2,2,2,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[6,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[4,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[4,3]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[7]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[4,3]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[6,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[3,3,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[7]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>[6,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[5,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[7]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[4,3]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[7]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[3,2,2]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[5,2]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[5,2]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>[4,2,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>[3,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>[5,2]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[3,2,2]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[4,1,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[4,2,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[2,2,1,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[2,2,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[5,2]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[7]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[5,2]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[4,3]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[3,2,2]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[4,3]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[7]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[5,2]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[5,2]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[7]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[3,2,2]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[5,2]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[4,3]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[3,2,2]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[4,2,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[6,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[4,2,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[4,2,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[2,2,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[1,2,3,4,6,7,8,5]=>[4,1,1,1,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6]=>[2,2,1,1,1,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[1,2,3,4,7,8,6,5]=>[4,1,1,1,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>[4,1,1,1,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[1,2,3,4,8,6,7,5]=>[2,1,1,1,1,1,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>[4,1,1,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>[2,2,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,4]=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>[4,1,1,1,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>[5,1,1,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[1,2,3,5,8,6,7,4]=>[3,1,1,1,1,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[1,2,3,5,8,7,6,4]=>[3,2,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[1,2,3,6,7,8,4,5]=>[5,1,1,1]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[1,2,3,6,8,7,4,5]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[1,2,3,6,7,8,5,4]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[1,2,3,7,8,4,5,6]=>[5,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[1,2,3,7,8,4,6,5]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[1,2,3,7,8,5,6,4]=>[5,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[1,2,3,7,8,6,4,5]=>[2,2,1,1,1,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[1,2,3,7,8,6,5,4]=>[4,1,1,1,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>[5,1,1,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>[4,1,1,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[1,2,3,8,4,6,7,5]=>[3,1,1,1,1,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>[5,1,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[1,2,3,8,5,6,7,4]=>[2,1,1,1,1,1,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[1,2,3,8,5,7,6,4]=>[2,2,1,1,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[1,2,3,8,6,7,4,5]=>[5,1,1,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[1,2,3,8,6,7,5,4]=>[3,2,1,1,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>[3,2,1,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>[5,1,1,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[1,2,3,8,7,5,6,4]=>[3,2,1,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>[4,1,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>[2,2,1,1,1,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[1,2,4,5,8,6,7,3]=>[4,1,1,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[1,2,4,6,7,8,5,3]=>[4,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[1,2,4,6,8,7,5,3]=>[6,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[1,2,4,8,5,6,7,3]=>[3,1,1,1,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[1,2,4,8,7,6,5,3]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,2,5,6,7,8,3,4]=>[3,3,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,2,5,6,8,7,3,4]=>[6,1,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[1,2,5,7,8,6,3,4]=>[5,1,1,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[1,2,5,8,6,7,4,3]=>[6,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[1,2,6,7,8,3,4,5]=>[2,2,2,1,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,2,6,8,7,3,4,5]=>[4,2,1,1]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[1,2,6,7,8,3,5,4]=>[4,2,1,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[1,2,6,7,8,5,3,4]=>[6,1,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[1,2,6,7,8,5,4,3]=>[4,2,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,2,7,8,3,4,5,6]=>[3,3,1,1]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[1,2,7,8,3,4,6,5]=>[6,1,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[1,2,7,8,3,5,6,4]=>[4,2,1,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,2,7,8,3,6,4,5]=>[5,1,1,1]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[1,2,7,8,3,6,5,4]=>[3,2,1,1,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4]=>[2,2,1,1,1,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,2,7,8,6,3,4,5]=>[6,1,1]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[1,2,7,8,6,5,3,4]=>[2,2,2,1,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>[6,1,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>[5,1,1,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[1,2,8,3,4,6,7,5]=>[4,1,1,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[1,2,8,3,5,6,7,4]=>[3,1,1,1,1,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[4,6,7,5,3,8,2,1]=>[1,2,8,3,5,7,6,4]=>[3,2,1,1,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>[4,2,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[1,2,8,4,5,6,7,3]=>[2,1,1,1,1,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[1,2,8,4,6,7,5,3]=>[3,2,1,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[1,2,8,4,7,6,5,3]=>[2,2,1,1,1,1]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[1,2,8,6,7,3,5,4]=>[4,2,1,1]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[1,2,8,6,7,5,3,4]=>[6,1,1]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[1,2,8,6,7,5,4,3]=>[4,2,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>[6,1,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[1,2,8,7,5,6,3,4]=>[4,1,1,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[1,2,8,7,5,6,4,3]=>[2,2,1,1,1,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>[2,2,2,1,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[1,3,4,5,8,6,7,2]=>[5,1,1,1]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[1,3,4,5,8,7,6,2]=>[5,2,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>[5,2,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[1,3,4,8,5,6,7,2]=>[4,1,1,1,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[1,3,4,8,7,6,5,2]=>[4,2,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>[7,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[1,3,5,7,8,6,4,2]=>[4,2,1,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[1,3,5,8,7,6,4,2]=>[6,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[2,4,5,8,7,6,3,1]=>[1,3,6,7,8,5,4,2]=>[5,2,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[1,3,6,8,7,5,4,2]=>[7,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[1,3,7,8,4,6,5,2]=>[6,1,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[1,3,7,8,5,6,4,2]=>[5,1,1,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[1,3,8,4,5,6,7,2]=>[3,1,1,1,1,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[2,5,7,6,4,8,3,1]=>[1,3,8,4,6,7,5,2]=>[3,3,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[1,3,8,5,6,7,4,2]=>[4,3,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[1,3,8,5,7,6,4,2]=>[3,3,1,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[1,3,8,7,5,6,4,2]=>[3,2,1,1,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[1,3,8,7,6,5,4,2]=>[3,2,2,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[1,4,6,7,8,5,3,2]=>[7,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[1,4,6,8,7,5,3,2]=>[4,3,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>[3,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[1,4,8,7,6,5,3,2]=>[5,2,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,5,6,7,8,2,3,4]=>[7,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[1,5,7,8,6,2,3,4]=>[3,2,2,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,5,8,7,6,2,3,4]=>[4,3,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[1,5,6,7,8,2,4,3]=>[5,2,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[1,5,8,7,6,2,4,3]=>[3,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[1,5,6,7,8,3,4,2]=>[3,2,2,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[1,5,7,8,6,3,4,2]=>[7,1]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[2,4,3,7,6,8,5,1]=>[1,5,8,6,7,3,4,2]=>[7,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[1,5,8,7,6,3,4,2]=>[5,2,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,5,6,7,8,4,2,3]=>[7,1]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[3,2,4,6,8,7,5,1]=>[1,5,7,8,6,4,2,3]=>[7,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[1,5,6,7,8,4,3,2]=>[4,3,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>[7,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[1,6,8,7,2,3,4,5]=>[5,2,1]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[1,6,7,8,2,3,5,4]=>[5,2,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[1,6,7,8,2,5,3,4]=>[3,2,2,1]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[1,6,8,7,2,5,4,3]=>[3,2,2,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[1,6,7,8,4,5,3,2]=>[5,2,1]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[1,6,8,7,4,5,3,2]=>[7,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[1,6,8,7,5,2,3,4]=>[4,2,1,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[1,6,7,8,5,3,4,2]=>[6,1,1]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[2,4,3,5,7,8,6,1]=>[1,6,8,7,5,3,4,2]=>[4,2,1,1]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>[4,2,1,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[1,6,8,7,5,4,3,2]=>[6,1,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>[7,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,7,8,2,3,6,4,5]=>[3,3,1,1]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[1,7,8,2,3,6,5,4]=>[6,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[1,7,8,2,4,5,6,3]=>[5,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[1,7,8,3,4,5,6,2]=>[7,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[1,7,8,3,5,6,4,2]=>[5,1,1,1]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[1,7,8,3,6,5,4,2]=>[5,2,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[1,7,8,4,5,6,2,3]=>[2,2,1,1,1,1]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[3,2,5,6,4,8,7,1]=>[1,7,8,4,6,5,2,3]=>[2,2,2,1,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[1,7,8,5,6,3,4,2]=>[7,1]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[1,7,8,5,6,4,2,3]=>[3,2,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[1,7,8,6,2,3,4,5]=>[7,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[1,7,8,6,2,5,4,3]=>[5,2,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[1,7,8,6,3,4,5,2]=>[5,2,1]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>[1,7,8,6,3,5,4,2]=>[7,1]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[2,3,5,4,6,8,7,1]=>[1,7,8,6,4,5,3,2]=>[4,3,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>[4,2,1,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[7,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[1,8,2,3,4,6,7,5]=>[5,1,1,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>[5,2,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[1,8,2,3,5,6,7,4]=>[4,1,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[1,8,2,4,5,6,7,3]=>[3,1,1,1,1,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[1,8,2,4,7,5,6,3]=>[3,3,1,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[1,8,2,4,7,6,5,3]=>[3,2,1,1,1]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[1,8,2,5,7,6,3,4]=>[6,1,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[1,8,2,5,7,6,4,3]=>[3,3,1,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>[7,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>[4,2,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[1,8,2,7,4,5,6,3]=>[4,3,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,8,2,7,5,6,3,4]=>[5,1,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>[5,2,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[1,8,2,7,6,4,5,3]=>[4,3,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>[3,2,2,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[1,8,3,4,6,7,5,2]=>[3,2,1,1,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[1,8,3,5,7,6,4,2]=>[3,2,1,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[1,8,3,6,7,4,5,2]=>[2,2,2,1,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[2,6,5,4,7,3,8,1]=>[1,8,3,7,4,5,6,2]=>[4,2,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[1,8,3,7,5,6,4,2]=>[2,2,1,1,1,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[1,8,3,7,6,4,5,2]=>[4,2,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[1,8,3,7,6,5,4,2]=>[2,2,2,1,1]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,8,4,5,7,6,2,3]=>[6,1,1]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[1,8,4,6,7,5,2,3]=>[7,1]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,8,4,7,6,5,2,3]=>[5,2,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[1,8,4,5,6,7,3,2]=>[5,2,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[1,8,4,7,6,5,3,2]=>[3,2,2,1]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[1,8,5,7,6,2,3,4]=>[7,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,8,6,7,2,3,4,5]=>[3,2,2,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,8,6,7,2,5,3,4]=>[7,1]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[1,8,6,7,2,5,4,3]=>[5,2,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[1,8,6,7,3,4,5,2]=>[5,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,8,6,7,4,5,2,3]=>[7,1]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[1,8,6,7,4,5,3,2]=>[5,2,1]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,8,6,7,5,2,3,4]=>[6,1,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[1,8,6,7,5,3,4,2]=>[2,2,2,1,1]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[1,8,6,7,5,4,3,2]=>[4,2,1,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>[4,3,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>[6,1,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[1,8,7,2,4,5,6,3]=>[7,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>[7,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[1,8,7,2,6,4,5,3]=>[7,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[1,8,7,3,4,5,6,2]=>[5,2,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[2,5,6,4,3,7,8,1]=>[1,8,7,3,4,6,5,2]=>[4,2,1,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[3,2,6,5,4,7,8,1]=>[1,8,7,4,5,6,2,3]=>[4,1,1,1,1]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[1,8,7,4,6,5,3,2]=>[2,2,2,1,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[1,8,7,5,6,4,3,2]=>[3,2,2,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>[4,3,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[7,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[1,8,7,6,4,5,3,2]=>[3,2,2,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>[4,2,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>[6,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[2,2,2,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>[8]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>[7,1]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[2,3,4,5,8,6,7,1]=>[6,1,1]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[2,3,4,5,8,7,6,1]=>[6,2]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[2,3,4,6,7,8,5,1]=>[6,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,3,4,8,5,6,7,1]=>[5,1,1,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[2,3,4,8,5,7,6,1]=>[5,2,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[2,3,4,8,6,7,5,1]=>[5,3]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,3,4,8,7,5,6,1]=>[5,3]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,5,1]=>[5,2,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>[8]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[2,3,5,7,8,6,4,1]=>[5,2,1]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[2,3,5,8,6,7,4,1]=>[8]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[2,3,5,8,7,6,4,1]=>[7,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,3,8,4,5,6,7,1]=>[4,1,1,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[2,3,8,5,7,6,4,1]=>[4,3,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,3,8,7,4,5,6,1]=>[4,4]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[2,3,8,7,6,5,4,1]=>[4,2,2]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>[4,4]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[2,4,7,8,5,6,3,1]=>[4,2,1,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[2,4,8,5,7,6,3,1]=>[7,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[2,4,8,7,5,6,3,1]=>[6,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>[6,2]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,5,8,6,7,3,4,1]=>[8]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[2,5,6,7,8,4,3,1]=>[4,4]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,6,7,8,5,3,4,1]=>[7,1]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[2,7,8,4,5,6,3,1]=>[5,1,1,1]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,7,8,5,6,3,4,1]=>[8]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[2,7,8,6,3,5,4,1]=>[8]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[2,8,3,5,7,6,4,1]=>[3,3,1,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,6,5,4,7,3,8,2]=>[2,8,3,7,4,5,6,1]=>[4,3,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[2,8,3,7,4,6,5,1]=>[3,3,1,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>[2,8,3,7,5,6,4,1]=>[3,2,1,1,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[2,8,5,6,7,4,3,1]=>[3,3,2]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[2,8,7,3,4,5,6,1]=>[5,3]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[2,8,7,5,6,4,3,1]=>[3,3,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,8,7,6,3,4,5,1]=>[3,3,2]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[3,2,2,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[4,4]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[3,4,5,8,7,6,1,2]=>[4,3,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[3,4,8,5,6,7,1,2]=>[8]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[3,4,8,5,7,6,1,2]=>[7,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[3,4,8,7,5,6,1,2]=>[6,1,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[3,4,8,7,6,5,1,2]=>[6,2]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[3,5,6,7,8,4,1,2]=>[5,3]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[3,6,7,8,5,4,1,2]=>[4,3,1]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[3,8,7,4,5,6,1,2]=>[3,2,1,1,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>[3,2,2,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[3,4,5,8,6,7,2,1]=>[8]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[3,4,8,7,5,6,2,1]=>[3,3,1,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,6,5,2,1]=>[3,3,2]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>[8]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[3,5,7,8,6,4,2,1]=>[8]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,5,8,7,6,4,2,1]=>[5,3]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[3,6,7,8,4,5,2,1]=>[8]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[3,7,8,4,5,6,2,1]=>[3,2,1,1,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[3,7,8,5,6,4,2,1]=>[3,3,2]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[3,8,4,5,6,7,2,1]=>[8]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[3,8,5,7,6,4,2,1]=>[8]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[3,8,7,5,6,4,2,1]=>[5,3]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[5,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[4,7,8,5,6,1,2,3]=>[4,2,2]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[4,8,6,7,5,1,2,3]=>[7,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[4,8,7,5,6,1,2,3]=>[4,4]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,8,7,6,5,1,2,3]=>[4,3,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[4,5,8,6,7,1,3,2]=>[5,3]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[4,5,8,7,6,1,3,2]=>[8]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[4,6,7,8,5,1,3,2]=>[5,2,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[4,7,8,5,6,1,3,2]=>[4,4]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[4,8,7,5,6,1,3,2]=>[4,2,2]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,8,7,6,5,1,3,2]=>[3,2,2,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[4,8,5,6,7,2,3,1]=>[5,3]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[5,2,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2]=>[3,3,2]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>[6,2]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[4,5,7,8,6,3,1,2]=>[8]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[4,8,6,7,5,3,1,2]=>[3,2,2,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[4,8,7,6,5,3,1,2]=>[5,2,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>[6,2]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,2,1]=>[3,3,2]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[4,8,7,5,6,3,2,1]=>[8]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[7,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[2,2,2,2]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[5,6,8,7,1,2,3,4]=>[4,2,2]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[5,7,8,6,1,2,3,4]=>[6,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[5,8,6,7,1,2,3,4]=>[6,2]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,8,7,6,1,2,3,4]=>[4,2,2]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[5,6,7,8,1,2,4,3]=>[4,2,2]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>[2,2,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[5,8,6,7,1,2,4,3]=>[4,2,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,8,7,6,1,2,4,3]=>[6,2]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[5,6,7,8,1,3,4,2]=>[6,2]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[5,7,8,6,1,3,4,2]=>[6,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>[2,2,2,2]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[5,8,7,6,1,3,4,2]=>[4,2,2]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[5,6,7,8,1,4,2,3]=>[6,2]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[5,6,8,7,1,4,2,3]=>[4,2,2]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>[2,2,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[5,8,6,7,1,4,2,3]=>[6,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,8,7,6,1,4,2,3]=>[4,2,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[5,6,7,8,1,4,3,2]=>[4,2,2]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[5,6,8,7,1,4,3,2]=>[6,2]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[5,7,8,6,1,4,3,2]=>[4,2,2]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[5,8,6,7,1,4,3,2]=>[4,2,2]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[2,2,2,2]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1]=>[8]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[5,7,8,6,2,3,4,1]=>[8]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[5,8,6,7,2,3,4,1]=>[4,2,2]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[5,8,7,6,2,3,4,1]=>[4,4]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,6,7,8,2,4,3,1]=>[6,2]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[5,6,8,7,2,4,3,1]=>[8]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[5,8,6,7,2,4,3,1]=>[4,4]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>[4,2,2]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[4,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,6,8,7,3,4,1,2]=>[8]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,7,8,6,3,4,1,2]=>[6,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,8,6,7,3,4,1,2]=>[6,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>[4,2,2]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1]=>[8]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[5,7,8,6,3,4,2,1]=>[4,2,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[5,8,6,7,3,4,2,1]=>[8]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[6,2]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3]=>[8]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,6,8,7,4,1,2,3]=>[6,2]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[5,7,8,6,4,1,2,3]=>[4,2,2]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[5,8,6,7,4,1,2,3]=>[8]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[5,8,7,6,4,1,2,3]=>[4,4]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[5,6,7,8,4,1,3,2]=>[6,2]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,8,6,7,4,1,3,2]=>[6,2]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>[4,2,2]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1]=>[4,2,2]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[5,7,8,6,4,2,3,1]=>[8]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[5,8,6,7,4,2,3,1]=>[8]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>[6,2]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2]=>[8]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[5,6,8,7,4,3,1,2]=>[4,4]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[5,8,6,7,4,3,1,2]=>[4,2,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>[6,2]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>[4,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[5,6,8,7,4,3,2,1]=>[8]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[5,7,8,6,4,3,2,1]=>[6,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[5,8,6,7,4,3,2,1]=>[6,2]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[8]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5]=>[8]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,8,7,1,2,3,4,5]=>[5,3]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[6,7,8,1,2,3,5,4]=>[5,3]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[6,7,8,1,2,4,5,3]=>[3,3,2]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[6,7,8,1,2,5,3,4]=>[8]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[6,7,8,1,2,5,4,3]=>[6,2]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[6,7,8,1,3,4,5,2]=>[5,3]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,8,7,1,3,4,5,2]=>[3,3,2]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[6,7,8,1,3,5,4,2]=>[8]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[6,7,8,1,4,5,2,3]=>[4,2,2]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[6,7,8,1,4,5,3,2]=>[4,4]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[6,7,8,1,5,2,3,4]=>[7,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,8,7,1,5,2,3,4]=>[5,2,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[6,7,8,1,5,2,4,3]=>[5,2,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[6,7,8,1,5,3,4,2]=>[7,1]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[6,7,8,1,5,4,3,2]=>[4,3,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>[3,2,2,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1]=>[8]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[6,8,7,2,3,4,5,1]=>[5,3]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[6,7,8,2,3,5,4,1]=>[5,3]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[6,8,7,2,4,5,3,1]=>[6,2]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>[5,2,1]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1]=>[6,2]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>[8]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4]=>[8]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[6,8,7,5,1,2,3,4]=>[6,2]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[6,7,8,5,1,2,4,3]=>[6,2]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[3,4,2,1,5,7,8,6]=>[6,8,7,5,1,2,4,3]=>[8]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[6,7,8,5,1,4,2,3]=>[4,2,2]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[6,8,7,5,1,4,2,3]=>[4,4]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,7,8,5,1,4,3,2]=>[4,4]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>[4,2,2]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1]=>[4,4]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[6,7,8,5,3,4,1,2]=>[8]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[2,2,2,2]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[6,8,7,5,4,1,2,3]=>[4,2,2]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[2,2,2,2]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1]=>[4,2,2]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[6,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[4,4]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,8,1,2,3,4,6,5]=>[8]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,8,1,2,3,6,4,5]=>[7,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,8,1,2,3,6,5,4]=>[4,3,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,8,1,2,4,5,6,3]=>[8]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,8,1,2,4,6,5,3]=>[7,1]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,8,1,2,5,6,3,4]=>[3,3,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[7,8,1,2,6,3,4,5]=>[8]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,8,1,2,6,3,5,4]=>[5,3]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,8,1,2,6,5,3,4]=>[3,3,2]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,8,1,3,4,5,6,2]=>[6,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,8,1,4,5,6,3,2]=>[3,2,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,8,1,6,2,3,4,5]=>[5,3]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[7,8,1,6,2,4,5,3]=>[6,2]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>[3,2,2,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,2,1,1,1,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[7,8,3,4,6,5,1,2]=>[2,2,2,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[7,8,3,5,6,4,1,2]=>[3,2,2,1]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[7,8,3,6,5,4,1,2]=>[2,2,2,1,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,2,5,6,4,3,8,7]=>[7,8,3,4,6,5,2,1]=>[4,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[4,4]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[7,8,5,6,1,2,4,3]=>[8]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[7,8,5,6,1,3,4,2]=>[6,2]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[7,8,5,6,1,4,2,3]=>[6,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>[4,2,2]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[7,8,5,6,2,3,4,1]=>[8]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[4,2,2]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[7,8,5,6,4,1,2,3]=>[8]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[2,3,1,4,6,5,8,7]=>[7,8,5,6,4,1,3,2]=>[6,2]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2]=>[4,2,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[4,4]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5]=>[3,3,2]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[7,8,6,1,2,4,5,3]=>[8]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[7,8,6,1,3,4,5,2]=>[6,2]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[7,8,6,1,3,5,4,2]=>[3,3,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[7,8,6,1,4,5,2,3]=>[8]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[7,8,6,1,5,2,3,4]=>[7,1]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>[5,2,1]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1]=>[8]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[7,8,6,2,3,5,4,1]=>[5,3]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2]=>[4,2,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1]=>[4,4]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[7,8,6,3,5,4,2,1]=>[4,3,1]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>[2,2,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4]=>[8]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[7,8,6,5,1,4,2,3]=>[8]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>[6,2]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>[8]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2]=>[4,2,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[4,4]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,2,2,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[4,2,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[8]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[8,1,2,3,4,6,7,5]=>[6,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>[6,2]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>[5,1,1,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[8,1,2,3,5,7,6,4]=>[5,2,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[8,1,2,3,6,7,5,4]=>[5,3]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>[6,2]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[8,1,2,3,7,5,6,4]=>[5,3]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>[5,2,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[8,1,2,4,5,6,7,3]=>[4,1,1,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[8,1,2,4,6,7,5,3]=>[4,3,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[8,1,2,4,7,6,5,3]=>[4,2,1,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>[4,4]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[8,1,2,6,7,3,5,4]=>[6,2]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[8,1,2,6,7,4,5,3]=>[4,2,2]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[8,1,2,6,7,5,3,4]=>[8]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[3,4,5,7,6,2,1,8]=>[8,1,2,6,7,5,4,3]=>[4,4]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>[8]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[8,1,2,7,3,5,6,4]=>[8]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>[5,2,1]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>[7,1]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[8,1,2,7,4,5,6,3]=>[4,4]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[8,1,2,7,4,6,5,3]=>[4,3,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>[6,2]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>[4,2,2]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[8,1,3,5,7,6,4,2]=>[3,3,1,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[8,1,3,6,7,4,5,2]=>[3,2,2,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[8,1,3,6,7,5,4,2]=>[4,3,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[2,6,5,4,7,3,1,8]=>[8,1,3,7,4,5,6,2]=>[4,3,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[8,1,3,7,4,6,5,2]=>[3,3,1,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[2,4,6,5,7,3,1,8]=>[8,1,3,7,5,6,4,2]=>[3,2,1,1,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[8,1,3,7,6,4,5,2]=>[4,3,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[8,1,4,5,6,7,2,3]=>[8]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[8,1,4,5,7,6,2,3]=>[7,1]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[8,1,4,6,7,5,2,3]=>[8]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[8,1,4,7,6,5,2,3]=>[6,2]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[8,1,4,5,6,7,3,2]=>[5,3]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[8,1,4,5,7,6,3,2]=>[4,3,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[8,1,5,6,7,2,3,4]=>[5,3]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[4,3,2,6,7,5,1,8]=>[8,1,5,7,6,2,3,4]=>[8]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[8,1,6,7,2,3,4,5]=>[4,2,2]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[8,1,6,7,2,3,5,4]=>[6,2]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[8,1,6,7,2,4,5,3]=>[8]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>[8,1,6,7,2,5,4,3]=>[6,2]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[8,1,6,7,4,5,2,3]=>[8]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[8,1,6,7,5,2,3,4]=>[7,1]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[8,1,6,7,5,4,3,2]=>[4,3,1]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[4,6,5,3,2,7,1,8]=>[8,1,7,2,3,5,6,4]=>[4,4]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>[7,1]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[8,1,7,2,4,5,6,3]=>[8]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[8,1,7,2,4,6,5,3]=>[7,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[8,1,7,2,5,6,3,4]=>[4,2,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>[8]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>[4,4]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[8,1,7,2,6,4,5,3]=>[8]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[8,1,7,3,6,4,5,2]=>[5,3]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[8,1,7,4,6,5,3,2]=>[3,2,2,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[8,1,7,5,6,3,4,2]=>[5,3]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[8,1,7,5,6,4,2,3]=>[5,3]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[8,1,7,5,6,4,3,2]=>[3,3,2]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>[4,4]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>[8]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[3,2,5,4,6,7,1,8]=>[8,1,7,6,4,5,2,3]=>[5,3]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[8,1,7,6,4,5,3,2]=>[3,3,2]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>[5,2,1]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[3,2,2,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[8,2,3,4,7,6,5,1]=>[2,2,1,1,1,1]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,6,5,4,7,3,2,8]=>[8,2,3,7,4,5,6,1]=>[4,2,1,1]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[8,2,3,7,5,6,4,1]=>[2,2,1,1,1,1]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,5,4,6,7,3,2,8]=>[8,2,3,7,6,4,5,1]=>[4,2,1,1]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[8,2,3,7,6,5,4,1]=>[2,2,2,1,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[8,2,4,6,7,5,3,1]=>[5,2,1]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,3,6,5,7,4,2,8]=>[8,2,4,7,5,6,3,1]=>[3,2,1,1,1]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[8,2,4,7,6,5,3,1]=>[3,2,2,1]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,3,4,7,6,5,2,8]=>[8,2,5,6,7,4,3,1]=>[3,2,2,1]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[8,2,6,7,5,3,4,1]=>[2,2,2,1,1]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[8,2,7,3,6,4,5,1]=>[5,2,1]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[8,2,7,4,5,6,3,1]=>[2,2,1,1,1,1]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[8,2,7,4,6,5,3,1]=>[2,2,2,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[8,2,7,5,6,3,4,1]=>[5,2,1]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>[8,2,7,5,6,4,3,1]=>[3,2,2,1]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[8,2,7,6,3,4,5,1]=>[3,2,2,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[2,2,2,1,1]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[2,1,6,5,4,7,3,8]=>[8,3,7,4,5,6,1,2]=>[5,1,1,1]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[8,3,7,6,4,5,1,2]=>[5,3]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[8,3,5,7,6,4,2,1]=>[6,2]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,2,6,5,4,7,3,8]=>[8,3,7,4,5,6,2,1]=>[3,2,1,1,1]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[8,3,7,5,6,4,2,1]=>[3,3,2]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[8,4,7,6,5,1,2,3]=>[7,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>[5,2,1]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[8,4,5,7,6,2,3,1]=>[6,2]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[8,4,7,5,6,2,3,1]=>[4,2,2]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>[3,2,2,1]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>[7,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[5,2,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4]=>[8]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[8,5,7,6,1,2,3,4]=>[6,2]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[3,4,2,1,6,7,5,8]=>[8,5,7,6,1,2,4,3]=>[8]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[8,5,6,7,1,4,2,3]=>[8]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[8,5,7,6,1,4,2,3]=>[6,2]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[8,5,6,7,1,4,3,2]=>[4,4]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>[4,2,2]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[2,2,2,2]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[8,5,7,6,2,3,4,1]=>[4,2,2]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[2,2,2,2]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]=>[8,5,6,7,3,4,1,2]=>[8]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1]=>[6,2]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3]=>[4,4]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[2,1,3,4,6,7,5,8]=>[8,5,7,6,4,3,1,2]=>[8]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1]=>[4,2,2]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[6,2]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5]=>[8]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[8,6,7,1,4,5,3,2]=>[6,2]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[8,6,7,1,5,2,3,4]=>[3,2,2,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[8,6,7,1,5,2,4,3]=>[5,2,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>[5,2,1]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1]=>[3,3,2]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[8,6,7,2,3,5,4,1]=>[6,2]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[8,6,7,2,5,3,4,1]=>[5,2,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1]=>[6,2]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3]=>[6,1,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[8,6,7,4,5,1,3,2]=>[4,2,1,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[2,2,2,1,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[4,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4]=>[4,2,2]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[8,6,7,5,1,4,2,3]=>[8]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>[6,2]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1]=>[6,2]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[2,2,2,2]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[4,2,2]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>[4,4]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>[4,3,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[8,7,1,2,4,5,6,3]=>[5,3]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>[5,3]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>[6,2]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[8,7,1,3,6,5,4,2]=>[6,2]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[3,2,5,6,4,1,7,8]=>[8,7,1,4,6,5,2,3]=>[3,2,2,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[8,7,1,5,6,2,3,4]=>[8]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[8,7,1,5,6,4,3,2]=>[5,3]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>[8]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>[5,3]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[8,7,1,6,2,4,5,3]=>[3,3,2]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>[5,3]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>[7,1]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[5,2,1]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[8,7,2,4,5,6,3,1]=>[3,2,1,1,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[8,7,2,6,4,5,3,1]=>[3,3,2]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[2,2,1,1,1,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[8,7,3,4,6,5,2,1]=>[2,2,2,1,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[8,7,3,5,6,4,2,1]=>[3,2,2,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,2,5,4,6,3,7,8]=>[8,7,3,6,4,5,2,1]=>[3,2,2,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[2,2,2,1,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[8,7,4,5,6,2,3,1]=>[6,2]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4]=>[8]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[2,4,3,1,6,5,7,8]=>[8,7,5,6,1,3,4,2]=>[8]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[8,7,5,6,1,4,2,3]=>[4,2,2]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>[6,2]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1]=>[6,2]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2]=>[4,2,2]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[2,2,2,2]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2]=>[4,4]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[4,2,2]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[6,2]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>[3,3,2]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[8,7,6,1,2,4,5,3]=>[5,3]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>[5,3]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>[8]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[8,7,6,1,3,4,5,2]=>[8]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[8,7,6,1,3,5,4,2]=>[5,3]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[8,7,6,1,4,5,2,3]=>[6,2]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[8,7,6,1,4,5,3,2]=>[8]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>[4,3,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>[7,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[8,7,6,1,5,3,4,2]=>[5,2,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>[5,2,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[7,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1]=>[6,2]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2]=>[4,4]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>[4,3,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1]=>[4,2,2]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[4,2,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[2,2,2,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[4,4]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>[8]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[8,7,6,5,1,3,4,2]=>[6,2]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>[6,2]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>[8]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1]=>[4,2,2]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[6,2]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2]=>[4,4]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[4,2,2]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[4,2,2]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>[6,2]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[4,2,2]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[4,2,2]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
cycle type
Description
The cycle type of a permutation as a partition.
searching the database
Sorry, this map was not found in the database.