Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-3
[.,.]=>[1]=>[1]=>[1,0]
[.,[.,.]]=>[2,1]=>[2,1]=>[1,1,0,0]
[[.,.],.]=>[1,2]=>[1,2]=>[1,0,1,0]
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0]
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[1,0,1,1,0,0]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[1,1,0,0,1,0]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,0,1,0,1,0]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,3,2]=>[1,0,1,1,1,0,0,0]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,2,1,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,2,1,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,4,1,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,6,1,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,6,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,6,1,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,1,6,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,1,6,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,1,6,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,1,2,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,1,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,1,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,1,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,1,5,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,1,5,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,7,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,7,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,7,5,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,7,6,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,7,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,7,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,7,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,1,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,2,1,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,1,2,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,1,2,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,1,2,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,2,1,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,2,1,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[4,3,1,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,3,1,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,1,3,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,1,3,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,2,3,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[5,3,2,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,4,2,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,2,1,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[5,2,1,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[5,4,3,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,3,1,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[5,4,1,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[5,4,1,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,1,4,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,1,4,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,1,2,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,1,3,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,5,3,2,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,5,4,2,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,2,4,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,2,1,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,3,1,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,1,3,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,5,1,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,5,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,1,5,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,1,2,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,1,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,1,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,1,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,1,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,6,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,6,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,6,5,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,2,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,6,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,6,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,2,1,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,2,1,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,3,1,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,1,3,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,5,3,2,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,2,4,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,4,3,2,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,3,2,1,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,3,2,1,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,3,2,1,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,3,2,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,5,4,2,1,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,4,2,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[8,2,1,7,6,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,2,1,7,3,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,2,1,7,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[8,3,1,2,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,4,1,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[8,7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[8,6,1,2,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[8,6,1,2,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[8,6,1,4,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,1,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,1,7,5,4,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,1,7,4,3,2,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,1,7,3,2,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,1,7,2,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,1,7,2,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,1,7,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[8,1,2,7,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[8,1,2,7,3,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,1,3,2,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[8,1,4,3,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[8,1,4,2,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[8,1,4,2,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,1,2,4,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[8,1,3,2,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[8,1,5,4,3,2,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,1,5,2,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,1,3,2,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[8,1,2,3,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[8,1,3,2,4,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[8,1,2,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,1,5,4,3,2,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,1,5,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,1,2,5,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,8,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[1,8,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[1,8,5,4,3,2,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[1,8,5,4,3,2,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[1,8,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[1,8,4,3,2,7,6,5]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,2,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,8,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[1,8,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,8,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[1,8,4,2,3,6,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,8,4,2,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[1,8,5,2,3,4,7,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[1,8,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[1,8,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[1,8,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,2,5,3,4,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[1,8,2,4,3,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,4,3,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[2,1,8,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,8,4,3,7,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,8,4,3,7,5,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,8,4,3,6,5,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,3,7,4,6,5]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,3,5,4,7,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,8,5,4,3,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,3,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,8,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,8,5,3,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[1,2,8,3,6,5,4,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[1,2,8,3,6,4,5,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,3,5,4,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[3,2,1,8,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[3,2,1,8,5,4,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[3,2,1,8,5,4,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[3,2,1,8,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,4,7,6,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[3,2,1,8,4,7,5,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,4,5,7,6]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,4,6,5,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,5,4,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,4,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,4,7,6,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,7,5,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,4,5,7,6]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,4,6,5,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,2,1,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[4,2,1,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,2,1,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[4,3,1,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,3,1,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,3,1,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,1,3,2,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,1,3,2,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,1,3,2,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,8,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,8,5,7,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,8,5,7,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,5,7,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,5,7,6]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,8,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,5,7,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,8,5,7,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,5,7,6]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,5,7,6]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,5,7,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[5,4,2,1,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[5,2,1,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[5,2,1,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[5,4,3,1,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[5,4,1,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,1,4,2,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[5,1,2,4,3,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[5,1,3,2,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,8,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,8,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[6,4,3,2,1,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[6,3,2,1,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[6,5,4,2,1,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[6,5,2,1,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[6,2,1,5,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[6,2,1,5,3,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[6,2,1,4,3,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[6,5,4,1,2,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[6,5,1,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[6,1,5,4,3,2,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,1,5,2,4,3,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,1,3,2,5,4,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,3,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,3,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,3,5,4,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,4,3,2,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,3,2,1,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,6,5,4,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[7,5,4,1,3,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,6,1,2,3,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,1,6,2,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[7,1,5,4,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[1,7,5,2,3,4,6,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[1,7,6,2,3,4,5,8]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,1,2,7,4,5,6,8]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,7,6,5,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[1,2,6,5,3,4,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,4,3,2,1,8,7,6,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,2,1,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,1,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,2,1,9,8,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,4,5,6,7,8]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,3,4,5,6,7,8]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,6,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,5,6,7,8,9]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,4,5,6,7,8,9]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,3,4,5,6,7,8,9]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,6,5,4,3,2,1,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[1,9,7,6,5,4,3,2,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[1,9,6,5,4,3,2,8,7]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[1,10,8,7,6,5,4,3,2,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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