Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]=>[1,1]
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]=>[2]
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>[1,1,1]
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>[2,1]
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[3,1,2]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[1,2]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>[1,4,3,2]=>[2,1,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,2,3,1]=>[4,1,3,2]=>[1,2,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>[3,1,4,2]=>[1,2,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[1,2,4,3]=>[3,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,2]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,4,1,2]=>[1,4,2,3]=>[2,2]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,2]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[4,1,2,3]=>[1,3]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[1,1,2]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[1,3,2,4]=>[2,2]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[3,1,2,4]=>[1,3]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[1,3]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,5,4,3,2]=>[2,1,1,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[5,1,4,3,2]=>[1,2,1,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[4,1,5,3,2]=>[1,2,1,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[5,4,1,3,2]=>[1,1,2,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,5,2,4,3]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[5,3,1,4,2]=>[1,1,2,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[5,1,2,4,3]=>[1,3,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[4,3,1,5,2]=>[1,1,2,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,4,2,5,3]=>[2,2,1]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,2,3,1,4]=>[4,1,2,5,3]=>[1,3,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[3,1,2,5,4]=>[1,3,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,2,3,5,4]=>[4,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,1,1,2]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[1,5,4,2,3]=>[2,1,2]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,5,2,3,1]=>[5,1,4,2,3]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,5,2,1,3]=>[4,1,5,2,3]=>[1,2,2]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[4,5,1,2,3]=>[1,2,5,3,4]=>[3,2]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,1,1,2]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,3,5,1,2]=>[1,5,3,2,4]=>[2,1,2]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,4,5,1,2]=>[1,5,2,3,4]=>[2,3]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,2]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,2,3,5,1]=>[5,1,3,2,4]=>[1,2,2]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,1,3]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,1,3]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,4]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[1,1,1,2]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[1,4,3,2,5]=>[2,1,2]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[4,1,3,2,5]=>[1,2,2]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[1,2,2]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,2,4,3,5]=>[3,2]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[1,1,3]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[1,4,2,3,5]=>[2,3]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[1,1,3]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,4]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[1,1,3]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,3,2,4,5]=>[2,3]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,4]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,4]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>[1,2,1,1,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>[1,2,1,1,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>[3,1,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>[1,1,2,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>[2,2,1,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>[1,1,2,1,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>[1,3,1,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>[1,1,2,1,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>[2,2,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>[1,3,1,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>[1,3,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>[4,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>[1,1,1,2,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>[2,1,2,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>[1,2,2,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>[1,2,2,1]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>[3,2,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>[1,1,1,2,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>[2,1,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>[1,1,3,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>[2,3,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>[1,1,1,2,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>[1,2,2,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>[1,1,3,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>[1,1,3,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>[1,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>[1,1,1,2,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>[2,1,2,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>[1,2,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>[1,2,2,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>[3,2,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>[1,1,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>[2,3,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>[1,1,3,1]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>[1,4,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>[1,1,3,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>[2,3,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>[1,4,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>[1,4,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>[5,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>[2,1,1,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>[1,2,1,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>[1,2,1,2]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>[3,1,2]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>[1,1,2,2]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>[2,2,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>[1,1,2,2]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>[1,3,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>[1,1,2,2]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>[2,2,2]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>[1,3,2]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>[1,3,2]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>[4,2]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>[2,1,1,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>[1,2,1,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>[1,2,1,2]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>[3,1,2]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,1,1,3]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>[2,1,3]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>[1,2,3]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>[1,2,3]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>[3,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>[2,1,1,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>[1,1,2,2]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>[2,2,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,1,1,3]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>[2,1,3]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,1,1,3]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>[2,1,3]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,1,4]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>[2,4]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>[1,2,1,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>[1,1,2,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>[1,1,2,2]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>[1,3,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,1,1,3]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>[1,2,3]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,1,1,3]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,1,4]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,1,1,3]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>[1,2,3]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,1,4]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,1,4]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,5]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>[2,1,1,2]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>[1,2,1,2]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>[1,2,1,2]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>[3,1,2]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>[1,1,2,2]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>[2,2,2]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>[1,1,2,2]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>[1,3,2]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>[1,1,2,2]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>[2,2,2]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>[1,3,2]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>[1,3,2]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>[4,2]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[1,1,1,3]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>[2,1,3]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>[1,2,3]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>[1,2,3]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>[3,3]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[1,1,1,3]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>[2,1,3]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[1,1,4]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>[2,4]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[1,1,1,3]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>[1,2,3]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[1,1,4]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[1,1,4]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,5]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>[2,1,3]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>[1,2,3]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[1,2,3]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>[3,3]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[1,1,4]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>[2,4]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[1,1,4]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,5]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[1,1,4]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>[2,4]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,5]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,5]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>[2,2,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>[1,1,2,1,1,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>[2,2,1,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>[1,3,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>[1,3,1,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>[2,1,2,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>[1,2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>[1,2,2,1,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>[1,1,1,2,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>[2,1,2,1,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>[2,3,1,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>[1,1,1,2,1,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>[1,2,2,1,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>[1,1,3,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>[1,1,3,1,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>[1,4,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>[2,1,2,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>[1,2,2,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>[1,2,2,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>[3,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>[1,1,3,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>[2,3,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>[1,1,3,1,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>[1,4,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>[1,1,3,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>[2,3,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>[1,4,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>[1,4,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>[5,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>[2,1,1,2,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>[1,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>[1,2,1,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>[3,1,2,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>[1,1,2,2,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>[1,1,2,2,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>[1,3,2,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>[1,1,2,2,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>[2,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>[1,3,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>[1,3,2,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>[4,2,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[1,1,1,1,2,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>[2,1,1,2,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>[1,2,1,2,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>[1,2,1,2,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>[3,1,2,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>[1,2,3,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>[1,2,3,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>[3,3,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[1,1,1,1,2,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>[2,1,1,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>[1,1,2,2,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>[2,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>[1,1,1,3,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>[2,1,3,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>[1,1,1,3,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>[2,1,3,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>[1,1,4,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>[2,4,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[1,1,1,1,2,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>[1,2,1,2,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>[1,1,2,2,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>[1,1,2,2,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>[1,3,2,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>[1,1,1,3,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>[1,2,3,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>[1,1,1,3,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>[1,1,4,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>[1,1,1,3,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>[1,2,3,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>[1,1,4,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>[1,1,4,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>[1,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>[2,1,1,2,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>[1,2,1,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>[1,2,1,2,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>[3,1,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>[1,1,2,2,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>[2,2,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>[1,1,2,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>[1,3,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>[1,1,2,2,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>[2,2,2,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>[1,3,2,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>[1,3,2,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>[4,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>[1,1,1,3,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>[2,1,3,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>[1,2,3,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>[1,2,3,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>[3,3,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>[1,1,1,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>[2,1,3,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>[1,1,4,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>[2,4,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>[1,1,1,3,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>[1,2,3,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>[1,1,4,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>[1,1,4,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>[1,5,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>[2,1,3,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>[1,2,3,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>[1,2,3,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>[3,3,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>[1,1,4,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>[2,4,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>[1,1,4,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>[1,5,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>[1,1,4,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>[2,4,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>[1,5,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>[1,5,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>[6,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>[2,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>[1,2,1,1,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>[1,2,1,1,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>[3,1,1,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>[1,1,2,1,2]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>[2,2,1,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>[1,1,2,1,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>[1,1,2,1,2]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>[2,2,1,2]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>[1,3,1,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>[1,3,1,2]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>[4,1,2]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>[1,1,1,2,2]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>[2,1,2,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>[1,2,2,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>[3,2,2]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>[1,1,1,2,2]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>[2,1,2,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>[1,1,3,2]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>[2,3,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>[1,1,1,2,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>[1,2,2,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>[1,1,3,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>[1,1,3,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>[1,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>[1,1,1,2,2]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>[2,1,2,2]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>[1,2,2,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>[1,2,2,2]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>[3,2,2]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>[1,1,3,2]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>[2,3,2]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>[1,1,3,2]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>[1,4,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>[1,1,3,2]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>[2,3,2]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>[1,4,2]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>[1,4,2]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>[5,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>[2,1,1,1,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>[1,2,1,1,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>[1,2,1,1,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>[3,1,1,2]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>[1,1,2,1,2]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>[2,2,1,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>[1,1,2,1,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>[1,3,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>[1,1,2,1,2]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>[2,2,1,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>[1,3,1,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>[1,3,1,2]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>[4,1,2]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>[2,1,1,3]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>[1,2,1,3]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>[1,2,1,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>[3,1,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>[2,2,3]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>[1,1,2,3]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>[1,3,3]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>[1,1,2,3]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>[2,2,3]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>[1,3,3]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>[1,3,3]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>[4,3]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>[2,1,1,1,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>[1,2,1,1,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>[1,2,1,1,2]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>[3,1,1,2]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>[1,1,1,2,2]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>[2,1,2,2]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>[1,2,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>[1,2,2,2]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>[3,2,2]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>[2,1,1,3]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>[1,2,1,3]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>[1,2,1,3]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>[3,1,3]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>[2,1,1,3]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>[1,2,1,3]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>[1,2,1,3]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>[3,1,3]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>[2,1,4]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>[1,2,4]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>[1,2,4]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>[3,4]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>[2,1,1,1,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>[1,1,2,1,2]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>[2,2,1,2]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[1,1,1,2,2]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>[2,1,2,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>[1,1,1,2,2]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>[2,1,2,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>[1,1,3,2]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>[2,3,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>[2,1,1,3]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>[1,1,2,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>[2,2,3]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>[2,1,1,3]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>[2,1,4]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>[2,1,1,3]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>[1,1,2,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>[2,2,3]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>[2,1,4]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>[2,1,4]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,1,5]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>[2,5]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>[1,2,1,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>[1,1,2,1,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>[1,1,2,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>[1,3,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[1,1,1,2,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>[1,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[1,1,1,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>[1,1,3,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>[1,1,1,2,2]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>[1,1,3,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>[1,1,3,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>[1,4,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>[1,2,1,3]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>[1,1,2,3]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>[1,1,2,3]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>[1,3,3]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>[1,2,1,3]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>[1,2,4]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>[1,1,2,3]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,1,5]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>[1,2,1,3]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>[1,3,3]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>[1,2,4]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,1,5]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,2,4]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,1,5]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[1,1,5]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>[1,2,1,1,2]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>[1,2,1,1,2]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>[1,1,2,1,2]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>[2,2,1,2]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>[1,1,2,1,2]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>[1,3,1,2]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>[1,1,2,1,2]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>[2,2,1,2]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>[1,3,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>[1,3,1,2]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>[4,1,2]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>[1,1,1,2,2]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>[2,1,2,2]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>[1,2,2,2]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>[1,2,2,2]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>[3,2,2]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>[1,1,1,2,2]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>[2,1,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>[1,1,3,2]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>[2,3,2]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>[1,1,1,2,2]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>[1,1,3,2]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>[1,1,3,2]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>[1,4,2]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>[1,1,1,2,2]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>[2,1,2,2]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>[1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>[1,2,2,2]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>[3,2,2]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>[1,1,3,2]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>[2,3,2]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>[1,1,3,2]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>[1,4,2]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>[1,1,3,2]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>[2,3,2]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>[1,4,2]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>[1,4,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>[5,2]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>[2,1,1,3]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>[1,2,1,3]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>[1,2,1,3]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>[3,1,3]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>[1,1,2,3]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>[2,2,3]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>[1,1,2,3]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>[1,3,3]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>[1,1,2,3]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>[2,2,3]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>[1,3,3]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>[1,3,3]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>[4,3]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>[2,1,1,3]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>[1,2,1,3]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>[1,2,1,3]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>[3,1,3]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>[2,1,4]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>[1,2,4]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>[1,2,4]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>[3,4]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>[2,1,1,3]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>[1,1,2,3]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>[2,2,3]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>[2,1,4]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>[2,1,4]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[1,1,5]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>[2,5]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>[1,2,1,3]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>[1,3,3]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>[1,2,4]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[1,1,5]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>[1,2,4]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[1,1,5]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[1,1,5]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,6]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>[1,2,1,3]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>[1,2,1,3]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>[3,1,3]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>[1,1,2,3]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>[2,2,3]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>[1,1,2,3]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>[1,3,3]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>[1,1,2,3]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>[2,2,3]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>[1,3,3]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>[1,3,3]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>[4,3]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>[2,1,4]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>[1,2,4]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>[1,2,4]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>[3,4]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>[2,1,4]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[1,1,5]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>[2,5]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>[1,2,4]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[1,1,5]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[1,1,5]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,6]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>[2,1,4]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[1,2,4]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[1,2,4]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>[3,4]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,1,5]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>[2,5]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[1,1,5]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,6]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[2,5]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,6]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,6]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>[1,1,2,1,1,1,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>[1,1,2,1,1,1,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,7,2,8,6,5,4,3]=>[2,2,1,1,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>[1,3,1,1,1,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[6,1,2,8,7,5,4,3]=>[1,3,1,1,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>[2,1,2,1,1,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>[1,2,2,1,1,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>[1,2,2,1,1,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>[3,2,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,2,3,5,1]=>[8,1,6,2,7,5,4,3]=>[1,2,2,1,1,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>[2,1,2,1,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>[1,2,2,1,1,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>[1,2,2,1,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>[2,3,1,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>[1,4,1,1,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>[1,1,3,1,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[1,6,2,3,8,7,5,4]=>[2,3,1,1,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>[1,4,1,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>[1,4,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>[1,2,1,2,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>[1,2,1,2,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>[2,2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>[1,3,2,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>[2,2,2,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>[1,3,2,1,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[8,7,5,6,2,1,3,4]=>[6,1,2,8,3,7,5,4]=>[1,3,2,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>[4,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>[1,1,1,1,2,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,7,5,4,6,3,1,2]=>[1,8,7,5,2,6,4,3]=>[2,1,1,2,1,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[8,7,5,4,6,2,3,1]=>[8,1,7,5,2,6,4,3]=>[1,2,1,2,1,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>[3,1,2,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>[1,2,3,1,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>[1,2,3,1,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>[3,3,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>[1,1,1,1,2,1,1]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[8,7,4,5,3,6,1,2]=>[1,8,6,2,3,7,5,4]=>[2,1,3,1,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>[2,1,3,1,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>[1,1,4,1,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>[2,4,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,1,7,3,2]=>[1,1,1,1,2,1,1]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>[1,2,1,2,1,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,2,4,6,1]=>[8,5,1,6,2,7,4,3]=>[1,1,2,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>[1,1,1,3,1,1]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>[1,5,1,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>[2,1,1,2,1,1]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>[3,1,2,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[7,6,1,5,2,8,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>[2,2,2,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>[1,1,2,2,1,1]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>[2,2,2,1,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>[1,3,2,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>[1,3,2,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>[4,2,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>[1,2,3,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>[3,3,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[8,7,4,3,5,2,1,6]=>[7,6,4,1,2,8,5,3]=>[1,1,1,3,1,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>[1,1,4,1,1]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[6,7,3,4,5,8,2,1]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>[2,4,1,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,2,5,1,6]=>[7,5,4,1,2,8,6,3]=>[1,1,1,3,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>[1,1,4,1,1]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>[1,5,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[6,5,4,1,2,8,7,3]=>[1,1,1,3,1,1]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[5,4,6,3,7,8,2,1]=>[8,7,4,2,1,3,5,6]=>[5,1,6,2,3,8,7,4]=>[1,2,3,1,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>[3,3,1,1]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>[2,4,1,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>[1,1,4,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>[1,5,1,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>[1,5,1,1]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>[1,5,1,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>[2,1,1,1,2,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>[1,1,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>[1,1,2,1,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>[1,3,1,2,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[8,6,7,5,3,2,1,4]=>[7,6,1,8,5,2,4,3]=>[1,1,2,1,2,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>[2,2,1,2,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[8,6,7,5,2,3,1,4]=>[7,1,2,8,6,3,5,4]=>[1,3,1,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>[4,1,2,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>[2,1,2,2,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>[1,2,2,2,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>[1,2,2,2,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>[3,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[8,6,7,4,3,5,2,1]=>[8,7,5,1,6,2,4,3]=>[1,1,1,2,2,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[8,6,7,3,4,5,1,2]=>[1,8,2,3,7,4,6,5]=>[2,3,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>[1,1,1,2,2,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>[1,2,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,6,7,3,4,2,5,1]=>[8,6,1,2,7,3,5,4]=>[1,1,3,2,1]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[8,6,7,2,3,4,5,1]=>[8,1,2,3,7,4,6,5]=>[1,4,2,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>[1,1,1,2,2,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>[1,2,2,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>[1,2,2,2,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[8,6,7,3,4,1,2,5]=>[1,7,2,3,8,4,6,5]=>[2,3,2,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[8,6,7,2,3,4,1,5]=>[7,1,2,3,8,4,6,5]=>[1,4,2,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>[1,1,3,2,1]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[8,6,7,3,1,2,4,5]=>[1,6,2,3,8,4,7,5]=>[2,3,2,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>[1,4,2,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>[1,4,2,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>[5,2,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>[2,1,1,1,2,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>[1,2,1,1,2,1]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[8,6,5,7,4,2,1,3]=>[7,1,8,6,4,2,5,3]=>[1,2,1,1,2,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>[3,1,1,2,1]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>[2,2,1,2,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>[1,1,2,1,2,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>[1,1,2,1,2,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>[2,2,1,2,1]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>[1,3,1,2,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>[4,1,2,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,5,6,7,4,2,3,1]=>[8,1,7,6,2,3,5,4]=>[1,2,1,3,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>[3,1,3,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>[1,1,2,3,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>[2,2,3,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>[1,1,2,3,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>[1,3,3,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>[1,1,2,3,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[8,5,6,7,2,3,1,4]=>[7,1,2,8,3,4,6,5]=>[1,3,3,1]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>[1,3,3,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>[4,3,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,2,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>[1,2,1,1,2,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[8,6,4,5,7,3,1,2]=>[1,8,7,2,5,3,6,4]=>[2,1,2,2,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>[1,2,2,2,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>[1,2,2,2,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>[3,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>[1,1,1,1,3,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[8,5,6,4,7,3,1,2]=>[1,8,7,5,2,3,6,4]=>[2,1,1,3,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,5,6,4,7,2,3,1]=>[8,1,7,5,2,3,6,4]=>[1,2,1,3,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>[3,1,3,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[8,5,4,6,7,3,2,1]=>[8,7,6,3,1,2,5,4]=>[1,1,1,1,3,1]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>[2,1,1,3,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,5,4,6,7,1,2,3]=>[1,2,8,5,3,4,7,6]=>[3,1,3,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[8,4,5,6,7,2,3,1]=>[8,1,7,2,3,4,6,5]=>[1,2,4,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>[3,4,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,2,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,6,4,5,3,7,2,1]=>[8,7,5,1,4,2,6,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>[1,1,1,2,2,1]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[1,1,1,1,3,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[8,5,4,3,6,7,2,1]=>[8,7,4,3,1,2,6,5]=>[1,1,1,1,3,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>[2,1,1,3,1]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[8,5,3,4,6,7,2,1]=>[8,7,1,4,2,3,6,5]=>[1,1,2,3,1]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>[2,2,3,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>[1,1,1,4,1]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>[2,1,4,1]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>[1,1,5,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>[2,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,2,1]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[8,6,5,3,4,2,7,1]=>[8,6,1,5,4,2,7,3]=>[1,1,2,1,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>[1,1,2,1,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[8,6,4,5,3,2,7,1]=>[8,6,5,1,4,2,7,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>[1,2,2,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>[1,1,1,2,2,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>[1,1,3,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>[1,2,2,2,1]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>[1,4,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>[1,1,1,1,3,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>[1,2,1,3,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[8,5,6,3,4,2,7,1]=>[8,6,1,5,2,3,7,4]=>[1,1,2,3,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[1,1,1,1,3,1]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,1,2,7,5]=>[1,1,1,1,3,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>[1,1,1,4,1]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[8,6,3,2,4,5,7,1]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>[1,1,1,4,1]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>[1,1,5,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,1,2,7,6]=>[1,1,1,1,3,1]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[8,5,4,2,3,6,7,1]=>[8,1,5,4,2,3,7,6]=>[1,2,1,3,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>[1,1,2,3,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>[1,3,3,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>[1,1,1,4,1]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[8,4,5,2,3,6,7,1]=>[8,1,5,2,3,4,7,6]=>[1,2,4,1]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[8,3,4,5,2,6,7,1]=>[8,5,1,2,3,4,7,6]=>[1,1,5,1]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>[1,1,1,4,1]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>[1,2,4,1]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>[1,1,5,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>[1,6,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,2,1]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>[2,1,1,1,2,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[7,1,6,5,4,2,8,3]=>[1,2,1,1,2,1]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>[1,2,1,1,2,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>[3,1,1,2,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>[1,1,2,1,2,1]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[6,7,4,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>[1,7,2,6,5,3,8,4]=>[2,2,1,2,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[8,6,5,3,2,4,1,7]=>[7,5,1,6,4,2,8,3]=>[1,1,2,1,2,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>[1,3,1,2,1]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>[1,1,2,1,2,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>[1,3,1,2,1]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[8,6,5,2,1,3,4,7]=>[5,1,2,7,6,3,8,4]=>[1,3,1,2,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>[4,1,2,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>[2,1,2,2,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>[1,2,2,2,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>[1,2,2,2,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>[3,2,2,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>[1,1,1,2,2,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[6,7,3,4,5,2,8,1]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>[2,3,2,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>[1,2,2,2,1]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>[1,1,3,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>[1,1,1,2,2,1]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>[2,1,2,2,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>[1,2,2,2,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>[3,2,2,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>[1,1,3,2,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>[2,3,2,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>[1,1,3,2,1]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>[1,4,2,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>[1,1,3,2,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>[5,2,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>[1,1,1,1,3,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>[1,2,1,3,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>[3,1,3,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>[1,1,2,3,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>[2,2,3,1]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>[1,3,3,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>[1,1,2,3,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>[2,2,3,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>[1,3,3,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>[1,3,3,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>[4,3,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>[1,1,1,1,3,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>[1,1,1,4,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[8,4,5,6,2,3,1,7]=>[7,1,6,2,3,4,8,5]=>[1,2,4,1]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[6,5,7,2,3,4,8,1]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>[1,2,4,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>[3,4,1]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,5,4,3,6,1,2,7]=>[1,7,5,4,2,3,8,6]=>[2,1,1,3,1]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[6,7,3,4,2,5,8,1]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>[2,2,3,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>[1,1,1,4,1]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>[2,1,4,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>[1,1,1,4,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>[2,1,4,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>[1,1,5,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>[2,5,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[8,5,4,3,2,6,1,7]=>[7,5,4,3,1,2,8,6]=>[1,1,1,1,3,1]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[7,4,5,3,2,6,8,1]=>[8,5,4,2,3,6,1,7]=>[7,1,5,4,2,3,8,6]=>[1,2,1,3,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>[1,1,2,3,1]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>[1,3,3,1]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>[1,2,4,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>[1,1,1,4,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>[1,1,5,1]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>[1,1,5,1]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>[1,6,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>[1,2,1,3,1]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>[1,2,6,5,3,4,8,7]=>[3,1,3,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>[2,2,3,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>[1,1,2,3,1]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>[2,2,3,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>[1,3,3,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>[4,3,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[8,4,5,2,3,1,6,7]=>[6,1,5,2,3,4,8,7]=>[1,2,4,1]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>[3,4,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>[1,1,5,1]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>[2,5,1]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[6,3,4,2,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>[1,2,4,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>[1,6,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,4,2,3,1,5,6,7]=>[5,1,4,2,3,6,8,7]=>[1,2,4,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[4,1,5,2,3,6,8,7]=>[1,2,4,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>[3,4,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,3,4,2,1,5,6,7]=>[5,4,1,2,3,6,8,7]=>[1,1,5,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>[2,5,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>[1,6,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>[1,1,5,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>[2,5,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>[1,6,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>[1,6,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>[7,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>[1,2,1,1,1,2]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>[1,2,1,1,1,2]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[7,8,6,5,4,1,2,3]=>[1,2,8,7,6,5,3,4]=>[3,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[7,8,6,5,3,4,2,1]=>[8,7,1,6,5,4,2,3]=>[1,1,2,1,1,2]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>[1,1,2,1,1,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>[1,1,2,1,1,2]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>[2,2,1,1,2]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>[1,3,1,1,2]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>[4,1,1,2]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>[1,1,1,2,1,2]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>[2,1,2,1,2]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>[1,1,1,2,1,2]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>[1,1,3,1,2]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>[2,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,3,1,2]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>[1,1,1,2,1,2]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>[1,1,3,1,2]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[7,8,6,3,2,4,5,1]=>[8,5,1,2,7,6,3,4]=>[1,1,3,1,2]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,3,1,2]=>[7,8,6,2,3,4,5,1]=>[8,1,2,3,7,6,4,5]=>[1,4,1,2]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>[1,1,1,2,1,2]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[7,8,6,4,2,1,3,5]=>[6,1,7,2,8,5,3,4]=>[1,2,2,1,2]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>[3,2,1,2]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[7,8,6,3,4,2,1,5]=>[7,6,1,2,8,5,3,4]=>[1,1,3,1,2]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>[2,3,1,2]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>[1,1,3,1,2]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>[2,3,1,2]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>[1,4,1,2]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>[1,4,1,2]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>[5,1,2]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>[1,2,1,2,2]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[7,8,5,6,4,1,2,3]=>[1,2,8,7,3,6,4,5]=>[3,1,2,2]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>[1,1,2,2,2]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>[1,3,2,2]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>[1,1,2,2,2]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>[1,3,2,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>[1,3,2,2]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>[4,2,2]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>[3,1,2,2]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>[2,1,3,2]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>[1,2,3,2]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[7,8,4,5,6,1,2,3]=>[1,2,8,3,4,7,5,6]=>[3,3,2]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>[1,1,1,1,2,2]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>[2,1,1,2,2]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>[1,1,2,2,2]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>[2,2,2,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>[2,1,3,2]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>[2,1,3,2]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>[1,1,4,2]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>[2,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>[1,1,1,1,2,2]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,3,7,1,2]=>[7,8,5,3,4,2,6,1]=>[8,6,1,5,2,7,3,4]=>[1,1,2,2,2]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>[1,1,1,3,2]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>[1,1,1,3,2]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[8,4,5,3,6,7,1,2]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>[1,2,3,2]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>[1,1,4,2]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>[1,1,4,2]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>[1,5,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>[1,1,1,1,2,2]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[7,8,5,4,3,1,2,6]=>[1,7,6,5,2,8,3,4]=>[2,1,1,2,2]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>[1,2,1,2,2]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>[3,1,2,2]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>[2,2,2,2]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>[1,3,2,2]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>[1,1,2,2,2]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>[2,2,2,2]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>[1,3,2,2]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>[4,2,2]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>[1,1,1,3,2]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>[1,2,3,2]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>[3,3,2]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>[1,1,4,2]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>[2,4,2]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>[1,1,1,3,2]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>[1,1,4,2]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>[1,5,2]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>[1,1,1,3,2]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>[2,1,3,2]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>[1,2,3,2]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>[3,3,2]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>[1,1,4,2]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>[2,4,2]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>[1,1,4,2]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>[1,5,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>[1,1,4,2]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>[2,4,2]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>[1,5,2]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>[1,5,2]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>[6,2]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>[2,1,1,1,1,2]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>[1,2,1,1,1,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>[1,2,1,1,1,2]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>[3,1,1,1,2]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>[1,1,2,1,1,2]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>[2,2,1,1,2]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[7,6,8,5,3,2,4,1]=>[8,6,1,7,5,3,2,4]=>[1,1,2,1,1,2]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[7,6,8,5,2,3,4,1]=>[8,1,2,7,6,4,3,5]=>[1,3,1,1,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>[1,1,2,1,1,2]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[7,6,8,5,3,1,2,4]=>[1,7,2,8,6,4,3,5]=>[2,2,1,1,2]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>[1,3,1,1,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>[1,3,1,1,2]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>[4,1,1,2]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>[1,1,1,2,1,2]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>[1,2,2,1,2]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>[1,2,2,1,2]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>[1,1,1,2,1,2]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[7,6,8,3,4,5,2,1]=>[8,7,1,2,6,4,3,5]=>[1,1,3,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>[1,1,1,2,1,2]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,2,1,3]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>[1,2,2,1,2]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>[1,1,3,1,2]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>[1,4,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>[1,1,1,2,1,2]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>[1,2,2,1,2]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>[3,2,1,2]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>[1,4,1,2]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>[1,1,3,1,2]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>[2,3,1,2]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>[1,4,1,2]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>[5,1,2]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>[2,1,1,1,3]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>[1,2,1,1,3]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>[3,1,1,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>[2,2,1,3]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>[1,1,2,1,3]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>[1,3,1,3]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>[1,1,2,1,3]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[6,7,8,5,2,3,1,4]=>[7,1,2,8,6,3,4,5]=>[1,3,1,3]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>[1,3,1,3]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>[4,1,3]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>[1,1,1,2,3]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>[2,1,2,3]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>[1,2,2,3]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>[3,2,3]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>[1,1,1,2,3]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>[2,1,2,3]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>[1,1,3,3]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,7,8,3,4,5,1,2]=>[1,8,2,3,7,4,5,6]=>[2,3,3]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[6,7,8,4,3,2,5,1]=>[8,6,5,1,7,2,3,4]=>[1,1,1,2,3]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>[1,2,2,3]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>[1,1,3,3]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>[1,1,3,3]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>[1,4,3]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>[1,1,1,2,3]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>[2,1,2,3]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>[1,2,2,3]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>[1,2,2,3]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>[3,2,3]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[6,7,8,3,4,2,1,5]=>[7,6,1,2,8,3,4,5]=>[1,1,3,3]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>[2,3,3]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>[1,1,3,3]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>[1,4,3]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>[1,1,3,3]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>[2,3,3]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>[1,4,3]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>[1,4,3]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>[5,3]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>[2,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>[1,2,1,1,1,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>[1,2,1,1,1,2]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>[3,1,1,1,2]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>[2,2,1,1,2]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>[1,3,1,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>[2,2,1,1,2]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[7,6,5,8,2,3,1,4]=>[7,1,2,8,5,4,3,6]=>[1,3,1,1,2]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[7,6,5,8,2,1,3,4]=>[6,1,2,8,5,4,3,7]=>[1,3,1,1,2]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>[4,1,1,2]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>[2,1,1,2,2]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>[1,2,1,2,2]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>[1,2,1,2,2]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>[3,1,2,2]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>[2,2,2,2]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[7,5,6,8,3,2,1,4]=>[7,6,1,8,2,4,3,5]=>[1,1,2,2,2]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>[2,2,2,2]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>[1,3,2,2]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[7,5,6,8,2,1,3,4]=>[6,1,2,8,3,5,4,7]=>[1,3,2,2]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>[4,2,2]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>[2,1,1,1,3]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>[1,2,1,1,3]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>[1,2,1,1,3]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[6,7,5,8,4,1,2,3]=>[1,2,8,7,5,3,4,6]=>[3,1,1,3]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>[1,1,2,1,3]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>[2,2,1,3]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>[1,1,2,1,3]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>[1,3,1,3]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>[1,1,2,1,3]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>[2,2,1,3]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>[1,3,1,3]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>[1,3,1,3]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>[4,1,3]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>[2,1,1,1,3]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>[1,2,1,1,3]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,5,7,8,4,1,2,3]=>[1,2,8,7,4,3,5,6]=>[3,1,1,3]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[6,5,7,8,3,4,2,1]=>[8,7,1,6,3,2,4,5]=>[1,1,2,1,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>[2,2,1,3]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>[1,1,2,1,3]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>[2,2,1,3]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[6,5,7,8,2,3,1,4]=>[7,1,2,8,4,3,5,6]=>[1,3,1,3]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>[1,3,1,3]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>[4,1,3]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>[2,1,1,4]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>[1,2,1,4]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>[1,2,1,4]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>[3,1,4]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>[1,1,2,4]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>[2,2,4]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>[1,1,2,4]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>[1,3,4]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>[1,1,2,4]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>[2,2,4]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>[1,3,4]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>[1,3,4]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>[2,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>[1,2,1,1,1,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>[1,2,1,1,1,2]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>[3,1,1,1,2]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>[2,1,2,1,2]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>[1,2,2,1,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[7,6,8,3,4,2,1,5]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>[1,2,2,1,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>[3,2,1,2]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>[1,2,1,2,2]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>[1,1,1,1,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>[1,2,1,2,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>[3,1,2,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>[1,1,1,3,2]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[7,4,5,6,8,2,1,3]=>[7,1,8,2,3,5,4,6]=>[1,2,3,2]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>[3,3,2]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>[1,2,1,1,3]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,7,5,4,8,1,2,3]=>[1,2,8,6,5,3,4,7]=>[3,1,1,3]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>[1,1,1,2,3]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>[2,1,2,3]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>[1,2,2,3]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>[3,2,3]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>[2,1,1,1,3]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>[1,2,1,1,3]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>[1,2,1,1,3]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,5,7,4,8,1,2,3]=>[1,2,8,6,4,3,5,7]=>[3,1,1,3]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>[1,2,1,4]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,6,7,4,8,1,2,3]=>[1,2,8,6,3,4,5,7]=>[3,1,4]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>[2,1,1,1,3]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>[3,1,1,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>[1,1,1,2,3]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>[3,2,3]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>[2,1,1,4]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>[3,1,4]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>[2,1,1,4]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[5,4,6,7,8,2,1,3]=>[7,1,8,3,2,4,5,6]=>[1,2,1,4]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>[3,1,4]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>[2,1,5]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>[1,2,5]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>[1,2,5]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>[3,5]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>[2,1,1,1,1,2]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[7,6,5,3,4,8,2,1]=>[8,7,1,5,4,3,2,6]=>[1,1,2,1,1,2]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[7,6,5,3,4,8,1,2]=>[1,8,2,6,5,4,3,7]=>[2,2,1,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[7,6,4,3,5,8,1,2]=>[1,8,5,2,6,4,3,7]=>[2,1,2,1,2]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>[2,3,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,2,2]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[7,5,6,4,3,8,1,2]=>[1,8,6,5,2,4,3,7]=>[2,1,1,2,2]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>[2,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[1,1,1,1,2,2]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>[1,1,1,3,2]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>[1,1,1,1,2,2]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>[2,1,1,2,2]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>[1,1,2,2,2]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>[2,2,2,2]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[7,3,4,5,6,8,2,1]=>[8,7,1,2,3,5,4,6]=>[1,1,4,2]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>[2,4,2]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>[1,1,1,2,3]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>[2,1,2,3]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,5,7,4,3,8,2,1]=>[8,7,5,4,2,1,3,6]=>[1,1,1,1,1,3]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>[2,1,1,1,3]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[5,6,7,4,3,8,1,2]=>[1,8,6,5,2,3,4,7]=>[2,1,1,4]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>[2,2,4]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>[2,1,2,3]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>[2,1,1,4]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>[2,1,1,4]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>[2,1,5]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>[2,1,1,1,3]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>[1,1,2,1,3]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,3,4,7,8,1,2]=>[1,8,2,5,4,3,6,7]=>[2,2,1,3]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>[2,1,2,3]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>[1,1,3,3]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>[2,3,3]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>[2,1,1,4]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>[2,2,4]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>[2,1,1,4]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[1,1,1,5]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[4,5,6,3,7,8,1,2]=>[1,8,5,2,3,4,6,7]=>[2,1,5]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>[2,1,1,4]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>[1,1,2,4]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>[2,2,4]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>[2,1,5]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>[2,1,5]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[1,1,6]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>[2,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>[1,2,1,1,1,2]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[1,1,2,1,1,2]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>[1,1,2,1,1,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,6,4,5,2,3,8,1]=>[8,1,6,2,5,4,3,7]=>[1,2,2,1,2]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>[1,1,1,2,1,2]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[8,6,3,4,5,2,1,7]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>[1,1,3,1,2]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>[1,2,2,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>[1,1,3,1,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>[1,4,1,2]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,5,6,4,2,3,8,1]=>[8,1,6,5,2,4,3,7]=>[1,2,1,2,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>[1,1,2,2,2]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[7,5,6,2,3,4,8,1]=>[8,1,2,6,3,5,4,7]=>[1,3,2,2]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[8,5,6,3,2,4,1,7]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>[1,2,1,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>[1,1,1,3,2]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>[1,2,3,2]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[7,5,4,3,6,2,8,1]=>[8,6,4,3,1,5,2,7]=>[1,1,1,1,2,2]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>[1,1,2,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>[1,1,1,3,2]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[8,6,2,3,4,5,1,7]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>[1,1,4,2]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>[1,2,1,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>[1,1,2,2,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,5,2,3,4,6,8,1]=>[8,1,2,5,3,6,4,7]=>[1,3,2,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,4,3,5,2,6,8,1]=>[8,5,3,1,2,6,4,7]=>[1,1,1,3,2]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>[1,1,1,3,2]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>[1,2,3,2]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>[1,1,4,2]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>[1,5,2]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,3,1,2,7]=>[6,7,5,4,2,3,8,1]=>[8,1,6,5,4,2,3,7]=>[1,2,1,1,3]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>[1,1,2,1,3]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[6,7,4,5,3,2,8,1]=>[8,6,5,1,4,2,3,7]=>[1,1,1,2,3]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>[1,2,2,3]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>[1,1,1,2,3]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>[1,1,3,3]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>[1,4,3]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[6,5,7,4,2,3,8,1]=>[8,1,6,5,3,2,4,7]=>[1,2,1,1,3]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>[1,1,2,1,3]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>[1,1,2,1,3]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>[1,2,1,4]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>[1,1,2,4]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>[1,3,4]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[6,5,4,7,2,3,8,1]=>[8,1,6,4,3,2,5,7]=>[1,2,1,1,3]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>[1,1,1,2,3]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>[1,2,2,3]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>[1,2,1,4]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,4,6,7,2,3,8,1]=>[8,1,6,3,2,4,5,7]=>[1,2,1,4]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,1,1,5]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>[1,2,5]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>[1,1,2,1,3]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[1,1,1,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>[1,1,1,2,3]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>[1,1,3,3]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>[1,1,2,4]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[1,1,6]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>[1,2,1,1,3]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[8,5,3,4,2,1,6,7]=>[6,5,3,4,2,7,8,1]=>[8,5,1,4,3,2,6,7]=>[1,1,2,1,3]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>[1,1,2,1,3]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>[1,3,1,3]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,4,5,2,3,7,8,1]=>[8,1,5,2,4,3,6,7]=>[1,2,2,3]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>[1,1,3,3]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>[1,4,3]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[8,4,5,3,1,2,6,7]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>[1,2,1,4]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>[1,3,4]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>[1,2,1,4]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>[1,1,1,5]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>[1,2,5]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[1,1,1,5]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,1,6]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[1,2,1,4]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>[1,1,2,4]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[5,3,2,4,6,7,8,1]=>[8,3,1,4,2,5,6,7]=>[1,1,2,4]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>[1,3,4]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[4,5,3,2,6,7,8,1]=>[8,4,3,1,2,5,6,7]=>[1,1,1,5]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[1,2,5]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[1,1,6]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[1,2,5]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,1,6]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[1,1,6]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,7]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>[2,1,1,1,1,2]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>[1,2,1,1,1,2]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>[6,1,7,5,4,3,2,8]=>[1,2,1,1,1,2]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[7,6,5,3,4,1,2,8]=>[1,7,2,6,5,4,3,8]=>[2,2,1,1,2]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>[1,1,2,1,1,2]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>[1,1,2,1,1,2]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>[6,1,2,7,5,4,3,8]=>[1,3,1,1,2]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[5,1,2,7,6,4,3,8]=>[1,3,1,1,2]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>[1,1,1,2,1,2]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>[1,2,2,1,2]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,1,5,3,2,8]=>[1,1,1,2,1,2]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>[1,1,3,1,2]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>[1,1,1,2,1,2]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>[1,2,2,1,2]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>[1,1,3,1,2]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>[1,4,1,2]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>[2,1,2,1,2]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[7,6,4,2,3,1,5,8]=>[6,1,5,2,7,4,3,8]=>[1,2,2,1,2]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>[1,2,2,1,2]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[6,5,3,4,7,2,1,8]=>[7,6,3,4,2,1,5,8]=>[6,5,1,2,7,4,3,8]=>[1,1,3,1,2]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[7,6,3,2,4,1,5,8]=>[6,4,1,2,7,5,3,8]=>[1,1,3,1,2]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>[1,4,1,2]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>[1,1,3,1,2]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[5,3,4,6,7,2,1,8]=>[7,6,2,3,1,4,5,8]=>[5,1,2,3,7,6,4,8]=>[1,4,1,2]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>[1,1,1,1,2,2]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,5,6,4,3,1,2,8]=>[1,7,6,5,2,4,3,8]=>[2,1,1,2,2]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>[1,2,1,2,2]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[7,5,6,4,1,2,3,8]=>[1,2,7,6,3,5,4,8]=>[3,1,2,2]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>[1,1,2,2,2]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,5,6,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>[2,2,2,2]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>[1,3,2,2]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,5,6,3,1,2,4,8]=>[1,6,2,7,3,5,4,8]=>[2,2,2,2]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[7,5,6,2,3,1,4,8]=>[6,1,2,7,3,5,4,8]=>[1,3,2,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[7,5,6,2,1,3,4,8]=>[5,1,2,7,3,6,4,8]=>[1,3,2,2]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,5,6,1,2,3,4,8]=>[1,2,3,7,4,6,5,8]=>[4,2,2]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>[1,1,1,1,2,2]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>[1,2,1,2,2]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[7,5,4,6,2,1,3,8]=>[6,1,7,4,2,5,3,8]=>[1,2,1,2,2]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,5,4,6,1,2,3,8]=>[1,2,7,5,3,6,4,8]=>[3,1,2,2]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>[1,1,1,3,2]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,4,5,6,3,1,2,8]=>[1,7,6,2,3,5,4,8]=>[2,1,3,2]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,4,5,6,2,3,1,8]=>[7,1,6,2,3,5,4,8]=>[1,2,3,2]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,4,5,6,2,1,3,8]=>[6,1,7,2,3,5,4,8]=>[1,2,3,2]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,4,5,6,1,2,3,8]=>[1,2,7,3,4,6,5,8]=>[3,3,2]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>[1,1,1,1,2,2]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[7,5,3,4,6,1,2,8]=>[1,7,2,5,3,6,4,8]=>[2,2,2,2]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>[1,1,1,3,2]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,3,4,5,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>[1,1,4,2]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>[1,2,1,2,2]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>[1,1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>[1,1,2,2,2]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[7,4,5,3,2,6,1,8]=>[7,5,4,1,2,6,3,8]=>[1,1,1,3,2]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>[1,2,3,2]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>[1,1,1,3,2]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>[1,5,2]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,1,7,2,8]=>[1,1,1,1,2,2]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[6,4,5,3,2,7,1,8]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>[1,2,1,2,2]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,3,4,1,2,6,8]=>[1,6,2,5,3,7,4,8]=>[2,2,2,2]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>[1,1,2,2,2]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>[6,1,2,5,3,7,4,8]=>[1,3,2,2]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>[1,1,2,2,2]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>[2,2,2,2]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>[1,3,2,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>[4,2,2]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[7,4,5,3,2,1,6,8]=>[6,5,4,1,2,7,3,8]=>[1,1,1,3,2]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,4,5,2,1,3,6,8]=>[5,1,6,2,3,7,4,8]=>[1,2,3,2]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,4,5,1,2,3,6,8]=>[1,2,6,3,4,7,5,8]=>[3,3,2]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>[1,1,1,3,2]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>[1,5,2]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>[1,1,1,3,2]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>[2,1,3,2]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>[3,3,2]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,3,4,1,2,5,6,8]=>[1,5,2,3,4,7,6,8]=>[2,4,2]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[7,2,3,4,1,5,6,8]=>[5,1,2,3,4,7,6,8]=>[1,5,2]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>[1,1,4,2]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>[2,4,2]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>[1,5,2]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>[1,5,2]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>[6,2]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[1,1,1,1,1,3]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>[2,1,1,1,3]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>[1,2,1,1,3]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>[1,3,1,3]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[6,7,5,2,1,3,4,8]=>[5,1,2,7,6,3,4,8]=>[1,3,1,3]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[6,7,5,1,2,3,4,8]=>[1,2,3,7,6,4,5,8]=>[4,1,3]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>[1,1,1,2,3]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>[1,2,2,3]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[7,6,4,3,5,1,2,8]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>[1,1,1,2,3]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[6,7,3,4,5,1,2,8]=>[1,7,2,3,6,4,5,8]=>[2,3,3]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>[1,1,1,2,3]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>[1,2,2,3]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[6,7,3,4,2,5,1,8]=>[7,5,1,2,6,3,4,8]=>[1,1,3,3]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[6,7,3,2,4,5,1,8]=>[7,4,1,2,6,3,5,8]=>[1,1,3,3]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[7,3,4,5,6,1,2,8]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>[1,4,3]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[6,7,4,3,2,1,5,8]=>[6,5,4,1,7,2,3,8]=>[1,1,1,2,3]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[6,7,4,2,3,1,5,8]=>[6,1,5,2,7,3,4,8]=>[1,2,2,3]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[6,7,3,4,2,1,5,8]=>[6,5,1,2,7,3,4,8]=>[1,1,3,3]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[6,7,3,4,1,2,5,8]=>[1,6,2,3,7,4,5,8]=>[2,3,3]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[6,7,3,2,4,1,5,8]=>[6,4,1,2,7,3,5,8]=>[1,1,3,3]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[6,7,2,3,4,1,5,8]=>[6,1,2,3,7,4,5,8]=>[1,4,3]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[6,7,3,1,2,4,5,8]=>[1,5,2,3,7,4,6,8]=>[2,3,3]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[5,3,4,6,7,1,2,8]=>[6,7,2,3,1,4,5,8]=>[5,1,2,3,7,4,6,8]=>[1,4,3]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[6,7,1,2,3,4,5,8]=>[1,2,3,4,7,5,6,8]=>[5,3]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>[1,1,1,1,1,3]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3,8]=>[6,1,7,5,3,2,4,8]=>[1,2,1,1,3]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[6,5,7,3,4,1,2,8]=>[1,7,2,6,4,3,5,8]=>[2,2,1,3]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>[1,1,2,1,3]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>[1,3,1,3]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,2,1,3,8]=>[6,5,7,2,3,1,4,8]=>[6,1,2,7,4,3,5,8]=>[1,3,1,3]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[6,5,7,1,2,3,4,8]=>[1,2,3,7,5,4,6,8]=>[4,1,3]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[5,6,7,4,2,3,1,8]=>[7,1,6,5,2,3,4,8]=>[1,2,1,4]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[1,2,7,6,3,4,5,8]=>[3,1,4]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[5,6,7,3,4,2,1,8]=>[7,6,1,5,2,3,4,8]=>[1,1,2,4]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[5,6,7,3,2,4,1,8]=>[7,5,1,6,2,3,4,8]=>[1,1,2,4]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>[1,3,4]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,7,3,1,2,4,8]=>[1,6,2,7,3,4,5,8]=>[2,2,4]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[5,6,7,2,3,1,4,8]=>[6,1,2,7,3,4,5,8]=>[1,3,4]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,6,7,2,1,3,4,8]=>[5,1,2,7,3,4,6,8]=>[1,3,4]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[5,6,7,1,2,3,4,8]=>[1,2,3,7,4,5,6,8]=>[4,4]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[6,5,4,7,2,3,1,8]=>[7,1,6,4,3,2,5,8]=>[1,2,1,1,3]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[5,6,4,7,3,2,1,8]=>[7,6,5,3,1,2,4,8]=>[1,1,1,1,4]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>[1,2,1,4]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,4,7,1,2,3,8]=>[1,2,7,5,3,4,6,8]=>[3,1,4]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[5,4,6,7,3,1,2,8]=>[1,7,6,3,2,4,5,8]=>[2,1,1,4]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[5,4,6,7,2,3,1,8]=>[7,1,6,3,2,4,5,8]=>[1,2,1,4]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[6,5,7,2,1,3,4,8]=>[5,4,6,7,2,1,3,8]=>[6,1,7,3,2,4,5,8]=>[1,2,1,4]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,4,6,7,1,2,3,8]=>[1,2,7,4,3,5,6,8]=>[3,1,4]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[4,5,6,7,3,1,2,8]=>[1,7,6,2,3,4,5,8]=>[2,1,5]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>[1,2,5]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[4,5,6,7,2,1,3,8]=>[6,1,7,2,3,4,5,8]=>[1,2,5]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8]=>[1,2,7,3,4,5,6,8]=>[3,5]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[6,5,4,3,7,1,2,8]=>[1,7,5,4,3,2,6,8]=>[2,1,1,1,3]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[6,4,3,5,7,1,2,8]=>[1,7,4,2,5,3,6,8]=>[2,1,2,3]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[6,3,4,5,7,1,2,8]=>[1,7,2,3,5,4,6,8]=>[2,3,3]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[5,6,3,4,7,1,2,8]=>[1,7,2,5,3,4,6,8]=>[2,2,4]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[6,7,2,1,3,4,5,8]=>[4,3,5,6,7,1,2,8]=>[1,7,3,2,4,5,6,8]=>[2,1,5]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[1,1,6]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8]=>[1,7,2,3,4,5,6,8]=>[2,6]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,3]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>[1,1,2,1,3]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>[1,1,3,3]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>[1,2,2,3]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>[1,1,3,3]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>[1,4,3]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>[1,1,2,4]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>[1,2,1,4]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>[1,1,2,4]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[4,3,5,6,2,7,1,8]=>[7,5,2,1,3,4,6,8]=>[1,1,1,5]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[1,1,6]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>[1,2,1,4]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>[1,3,4]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>[1,2,5]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[1,1,6]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[1,1,1,5]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[1,2,5]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[1,1,6]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[1,1,6]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,7]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>[2,1,1,1,3]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[5,1,6,4,3,2,7,8]=>[1,2,1,1,3]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>[1,1,2,1,3]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[6,5,2,3,4,1,7,8]=>[6,1,2,5,4,3,7,8]=>[1,3,1,3]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>[1,1,2,1,3]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[6,4,5,3,1,2,7,8]=>[1,6,5,2,4,3,7,8]=>[2,1,2,3]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[6,4,5,2,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>[1,2,2,3]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,3,5,1,2,7,8]=>[1,6,4,2,5,3,7,8]=>[2,1,2,3]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[6,3,4,5,2,1,7,8]=>[6,5,1,2,4,3,7,8]=>[1,1,3,3]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>[1,1,1,2,3]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>[1,4,3]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>[1,1,1,2,3]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>[2,1,2,3]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>[1,2,2,3]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>[3,2,3]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>[1,1,3,3]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>[2,3,3]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>[1,4,3]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[5,3]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7,8]=>[1,6,5,4,2,3,7,8]=>[2,1,1,4]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,6,4,2,1,3,7,8]=>[5,1,6,4,2,3,7,8]=>[1,2,1,4]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[5,6,3,4,2,1,7,8]=>[6,5,1,4,2,3,7,8]=>[1,1,2,4]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>[2,2,4]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[5,6,3,2,4,1,7,8]=>[6,4,1,5,2,3,7,8]=>[1,1,2,4]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[5,6,2,3,4,1,7,8]=>[6,1,2,5,3,4,7,8]=>[1,3,4]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,6,3,2,1,4,7,8]=>[5,4,1,6,2,3,7,8]=>[1,1,2,4]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[5,6,1,2,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>[4,4]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[1,1,1,1,4]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,4,6,3,1,2,7,8]=>[1,6,5,3,2,4,7,8]=>[2,1,1,4]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>[1,2,1,4]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[1,1,1,5]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[4,5,6,2,1,3,7,8]=>[5,1,6,2,3,4,7,8]=>[1,2,5]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>[3,5]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,4,3,6,1,2,7,8]=>[1,6,4,3,2,5,7,8]=>[2,1,1,4]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,1,6]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[3,4,5,6,1,2,7,8]=>[1,6,2,3,4,5,7,8]=>[2,6]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>[1,3,4]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[1,1,1,5]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[1,1,6]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>[1,1,1,5]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[6,2,1,3,4,5,7,8]=>[1,1,6]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[1,7]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[1,2,1,4]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[4,1,5,3,2,6,7,8]=>[1,2,1,4]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[1,1,2,4]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[2,2,4]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>[1,1,2,4]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[1,3,4]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[4,3,1,5,2,6,7,8]=>[1,1,2,4]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>[2,2,4]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>[1,3,4]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[3,1,2,5,4,6,7,8]=>[1,3,4]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[4,4]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>[1,2,5]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[3,5]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[1,1,1,5]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,1,6]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[2,6]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>[1,2,5]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,1,6]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[1,1,6]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,7]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[1,2,5]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[1,2,5]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[3,5]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,1,6]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[2,6]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[1,1,6]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,7]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[2,6]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,7]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>[4,1,1,1,1,1]
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1]
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>[6,1,1,1]
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>[7,1,1]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>[8,1]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,1,2]=>[1,9,2,8,7,6,5,4,3]=>[2,2,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>[4,1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[9,8,7,6,4,5,1,2,3]=>[1,2,9,3,8,7,6,5,4]=>[3,2,1,1,1,1]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1]
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[9,8,7,5,6,1,2,3,4]=>[1,2,3,9,4,8,7,6,5]=>[4,2,1,1,1]
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1]
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[9,8,6,7,1,2,3,4,5]=>[1,2,3,4,9,5,8,7,6]=>[5,2,1,1]
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>[7,1,1,1]
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,8,7]=>[6,2,1]
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>[8,1,1]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>[7,2]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[9,1]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>[1,1,1,2,1,1,1,1]
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>[1,1,1,1,2,1,1,1]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>[1,1,1,1,1,2,1,1]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>[1,3,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1,1]
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>[1,1,3,1,1,1,1]
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[9,6,7,5,4,3,2,1,8]=>[8,7,6,5,4,1,2,9,3]=>[1,1,1,1,1,3,1]
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>[1,1,1,1,1,1,2,1,1]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[1,1,1,1,1,1,3]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>[1,1,1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,2]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>[1,10,2,9,3,8,4,7,5,6]=>[2,2,2,2,2]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>[1,6,2,7,3,8,4,9,5,10]=>[2,2,2,2,2]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[1,12,2,11,3,10,4,9,5,8,6,7]=>[2,2,2,2,2,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[1,1,1,1,1,5]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[1,1,1,1,1,1,6]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,8]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,9]
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[1,1,7]
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>[1,7,1]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,10]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>[1,1,8]
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>[1,1,7]
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[1,2,6]
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,1]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>[2,7]
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>[3,6]
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>[4,5]
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>[5,4]
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>[6,3]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[1,1,7]
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>[2,8]
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>[1,2,6]
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>[3,7]
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>[4,6]
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>[5,5]
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[7,8,9,2,1,3,4,5,6]=>[5,1,2,3,4,9,6,7,8]=>[1,5,3]
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>[6,4]
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>[7,3]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>[8,2]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>[2,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>[2,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>[2,1,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>[2,1,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,2]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>[1,2,2,2,2,1]
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[1,2,2,2,2,2,1]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,2]
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,3]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,2]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,3]
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,4]
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[1,1,1,1,5]
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[1,1,1,6]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[1,1,7]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[1,8]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,3]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,4]
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[7,6,5,4,3,1,2,8,9]=>[6,7,5,4,3,2,1,8,9]=>[7,6,5,4,3,1,2,8,9]=>[1,1,1,1,1,4]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,5]
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>[1,1,1,1,5]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,6]
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>[1,1,1,6]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[1,1,1,7]
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>[1,1,7]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[1,1,8]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[1,8]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[1,9]
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[9,8,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>[1,1,1,2,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,2,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>[1,1,1,1,2,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,4,5,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>[1,1,1,1,1,2,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,2,1]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>[1,2,2,2,2,1]
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[10,8,9,6,7,4,5,2,1,3]=>[9,8,10,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,5,4,6]=>[1,2,2,2,1,2]
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>[1,7,1]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[1,10]
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>[1,1,7]
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>[2,1,6]
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>[1,7,1]
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>[2,6,1]
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>[1,8,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>[1,1,1,1,1,1,3]
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>[6,2,1]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>[7,2]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[2,7]
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[4,5]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[6,3]
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>[1,2,6]
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>[1,6,2]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[8,2]
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[1,8]
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[1,8]
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[1,8]
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,8]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[1,8]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[1,9]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[1,9]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[1,9]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[1,9]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[1,9]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[1,9]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,9]
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>[1,6,2]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,2,1]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>[1,1,1,1,1,1,3]
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>[2,1,1,1,1,1,2]
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,3]
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>[1,1,1,1,1,1,3]
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[1,1,1,1,1,1,1,3]
[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[7,2,3,4,5,6,8,9,1]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>[1,7,1]
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[4,5,1,2,3,6,7,8,9]=>[3,4,5,1,2,6,7,8,9]=>[1,5,2,3,4,6,7,8,9]=>[2,7]
[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]=>[7,8,1,2,3,4,5,6,9,10]=>[3,4,5,6,7,8,1,2,9,10]=>[1,8,2,3,4,5,6,7,9,10]=>[2,8]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,1,2,1]
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>[6,1,2]
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[7,8,1,2,3,4,5,6,9]=>[1,2,3,4,5,8,6,7,9]=>[6,3]
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>[2,1,1,1,1,1,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[1,1,8]
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>[1,2,8,7,6,5,4,3,9]=>[3,1,1,1,1,2]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>[1,1,1,1,1,1,1,1,2,1]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[1,1,1,6]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[1,1,1,1,5]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,4]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[1,1,7]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[1,1,1,7]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[1,1,1,1,6]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[1,1,1,1,1,5]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,4]
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>[2,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]
[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[7,6,5,4,3,8,9,2,1]=>[9,8,5,4,3,2,1,6,7]=>[7,6,5,4,1,2,9,8,3]=>[1,1,1,1,3,1,1]
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[3,4,5,6,7,8,2,1,9]=>[8,7,1,2,3,4,5,6,9]=>[1,1,7]
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[7,6,5,4,3,8,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>[1,1,1,1,1,1,3]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[1,1,1,1,1,1,1,3]
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>[1,6,2]
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>[2,7]
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[10,8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,9,8]=>[7,2,1]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,11,1,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[2,9]
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>[1,1,1,1,1,4]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,10,1]=>[10,3,1,2,4,5,6,7,8,9]=>[1,1,8]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>[1,1,1,1,1,1,1,3]
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>[1,6,1,1]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
inverse
Description
Sends a permutation to its inverse.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
searching the database
Sorry, this map was not found in the database.