Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-4
[.,.]=>[1]=>[1]=>[1]=>[1,0]
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]=>[1,1,0,0]
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]=>[1,0,1,0]
[.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[2,3,1]=>[1,1,0,1,0,0]
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[3,2,1]=>[1,1,1,0,0,0]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[1,1,0,0,1,0]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,0,1,0,1,0]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[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]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[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]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[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]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[7,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,7,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[6,5,4,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[6,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[6,7,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,7,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7,1,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[7,1,2,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[6,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[6,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[6,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[6,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[6,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[7,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[6,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[5,6,4,7,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[6,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[5,4,6,7,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,5,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[7,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[6,7,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[7,1,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[6,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[5,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[6,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[7,1,5,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[6,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[7,1,5,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[6,7,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[7,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[6,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[6,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7,1,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[7,1,6,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[7,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[7,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[7,1,6,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[7,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,1,6,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[6,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[6,2,4,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[5,6,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[6,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[6,2,5,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[6,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[6,4,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[6,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[6,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[6,5,3,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[6,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[6,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[6,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,7,2,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[7,2,1,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[6,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[6,5,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[6,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[6,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[7,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[7,2,1,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[7,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[6,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[6,4,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[6,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[6,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,7,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[6,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,7,3,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[6,4,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[6,5,4,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[6,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,7,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[6,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7,4,1,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,7,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[6,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[6,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,7,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[6,5,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[6,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7,6,1,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[7,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7,6,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7,6,1,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7,6,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[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]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,1,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,1,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,1,2,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,1,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,6,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[5,4,6,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,5,6,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[6,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[5,6,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[6,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1,5,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,5,1,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,5,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[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]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,5,1,3,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[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]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[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]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[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]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[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]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[7,6,8,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[7,8,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>[8,1,2,3,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[7,5,6,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[6,7,5,8,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[7,6,5,8,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[6,5,7,8,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,1,2,3,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[2,3,5,8,4,7,6,1]=>[7,6,8,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[6,7,8,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>[7,8,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>[8,1,2,3,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[2,3,7,6,4,8,5,1]=>[8,1,2,3,7,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[2,3,7,8,4,5,6,1]=>[8,1,2,3,7,6,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>[7,4,5,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[6,7,4,5,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>[7,4,6,5,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[6,5,7,4,8,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[2,3,8,7,5,6,4,1]=>[5,6,7,4,8,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[2,3,8,6,4,7,5,1]=>[7,5,4,6,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[2,3,8,7,4,6,5,1]=>[6,7,5,4,8,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[2,3,8,5,7,4,6,1]=>[7,6,4,5,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[7,6,5,4,8,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[6,4,5,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[5,6,4,7,8,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]=>[6,5,4,7,8,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>[5,4,6,7,8,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[4,5,6,7,8,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>[6,7,8,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>[8,1,2,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[7,8,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[6,7,5,8,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>[7,6,5,8,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[5,6,7,8,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[2,5,4,6,3,7,8,1]=>[8,1,2,5,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[7,6,8,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[6,7,8,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[6,7,8,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>[7,8,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,1,2,6,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,6,4,8,3,5,7,1]=>[7,8,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[2,7,6,5,8,4,3,1]=>[8,1,2,7,3,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[2,7,4,5,8,3,6,1]=>[8,1,2,7,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[2,8,5,7,4,6,3,1]=>[6,7,3,5,4,8,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[2,8,6,5,7,4,3,1]=>[7,3,6,4,5,8,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[5,6,4,7,3,8,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>[6,5,4,7,3,8,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[5,4,6,7,3,8,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[4,5,6,7,3,8,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[2,8,6,3,4,5,7,1]=>[6,5,4,3,7,8,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>[5,3,4,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[4,5,3,6,7,8,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[5,4,3,6,7,8,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[4,3,5,6,7,8,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[3,4,2,6,8,5,7,1]=>[7,8,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[7,5,6,8,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[6,7,5,8,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[5,6,7,8,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[8,1,3,2,5,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[8,1,3,2,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[7,6,8,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[6,7,8,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[3,6,2,7,4,5,8,1]=>[8,1,3,2,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[7,8,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[8,1,3,2,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[3,8,2,5,6,7,4,1]=>[7,4,5,6,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[7,4,6,5,8,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[6,5,7,4,8,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[4,5,6,7,8,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>[7,6,8,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[6,7,8,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[8,1,4,2,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[6,7,5,8,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[7,6,5,8,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>[6,5,7,8,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[5,6,7,8,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[6,7,8,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[8,1,4,3,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[4,7,2,3,6,8,5,1]=>[8,1,4,3,2,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[8,1,4,3,2,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[4,8,2,3,6,7,5,1]=>[7,5,6,8,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,6,7,8,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[7,6,8,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[8,1,5,2,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[7,6,8,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[5,4,2,6,3,8,7,1]=>[7,8,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[5,4,2,7,3,8,6,1]=>[8,1,5,3,2,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>[8,1,5,4,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[6,7,8,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>[7,6,8,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[7,8,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[8,1,6,2,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[7,8,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[6,5,2,8,4,3,7,1]=>[7,8,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[6,3,5,2,7,4,8,1]=>[8,1,6,4,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[7,8,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[8,1,7,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>[8,1,7,2,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[8,1,7,2,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[8,1,7,2,6,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[7,4,2,6,3,8,5,1]=>[8,1,7,5,3,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,1,7,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,1,7,6,2,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[8,1,7,6,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[8,1,7,6,3,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[8,1,7,6,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>[5,6,4,7,2,3,8,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,3,7,6,4,5,2,1]=>[6,5,4,7,2,3,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[4,5,6,7,2,3,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[7,2,4,3,6,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[7,2,6,3,4,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[6,3,5,4,7,2,8,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[4,5,6,3,7,2,8,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[6,7,3,2,4,5,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[6,7,3,2,5,4,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>[6,4,5,7,3,2,8,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[4,5,6,7,3,2,8,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>[6,5,7,4,2,3,8,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,3,7,2,4,6,5,1]=>[6,7,5,4,2,3,8,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>[7,6,4,2,3,5,8,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[3,4,5,6,2,7,8,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>[5,2,3,4,6,7,8,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[4,5,2,3,6,7,8,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[4,3,5,2,6,7,8,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[3,4,2,5,6,7,8,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[7,8,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>[6,7,8,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>[7,8,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[6,7,5,8,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[3,1,4,8,7,5,6,2]=>[7,6,5,8,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[6,5,7,8,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[5,6,7,8,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[7,8,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[3,1,8,7,4,6,5,2]=>[6,7,5,4,8,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>[7,6,4,5,8,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[4,5,6,7,8,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8,2,1,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,8,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[7,5,6,8,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[4,1,8,3,7,6,5,2]=>[6,7,5,8,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[7,6,5,8,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[6,5,7,8,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,6,7,8,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>[7,8,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[6,1,5,8,4,3,7,2]=>[7,8,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[7,8,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[7,8,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,1,4,6,3,8,5,2]=>[8,2,1,7,5,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[7,1,4,5,8,3,6,2]=>[8,2,1,7,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[8,2,1,7,6,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>[6,7,3,5,4,8,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[8,1,6,5,7,4,3,2]=>[7,3,6,4,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[6,4,5,7,3,8,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[8,1,7,5,4,6,3,2]=>[5,4,6,7,3,8,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[8,1,7,4,5,6,3,2]=>[4,5,6,7,3,8,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[8,1,6,3,4,7,5,2]=>[7,5,4,3,6,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>[7,6,3,4,5,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>[6,5,4,3,7,8,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[8,3,1,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[2,4,1,5,8,6,7,3]=>[6,7,8,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[8,3,1,2,4,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[7,8,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[7,5,6,8,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[6,7,5,8,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[2,4,1,8,6,5,7,3]=>[6,5,7,8,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[5,6,7,8,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[2,5,1,6,4,8,7,3]=>[7,8,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[2,5,1,7,4,8,6,3]=>[8,3,1,2,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[7,6,8,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[8,3,1,2,6,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[7,8,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[2,7,1,5,6,8,4,3]=>[8,3,1,2,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[2,8,1,5,7,6,4,3]=>[6,7,4,5,8,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[6,5,7,4,8,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[2,8,1,5,7,4,6,3]=>[7,6,4,5,8,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[4,5,6,7,8,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[8,3,2,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[7,8,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[4,1,2,5,8,7,6,3]=>[7,6,8,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[6,7,8,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[7,8,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[8,3,2,1,4,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[6,7,5,8,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[7,6,5,8,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[4,1,2,8,6,5,7,3]=>[6,5,7,8,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[5,6,7,8,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[7,8,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,3]=>[8,3,2,1,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[7,8,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[8,3,2,1,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[7,8,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[7,1,2,5,6,8,4,3]=>[8,3,2,1,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[8,3,2,1,7,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[8,3,2,1,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[7,4,5,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[8,1,2,5,7,6,4,3]=>[6,7,4,5,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[7,4,6,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[6,5,7,4,8,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[7,5,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[6,7,5,4,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[7,6,4,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[7,6,5,4,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[8,1,2,5,6,4,7,3]=>[6,4,5,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[8,1,2,6,5,4,7,3]=>[5,6,4,7,8,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[6,5,4,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,5,6,7,8,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]=>[7,6,8,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[7,8,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[8,4,1,2,3,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>[7,5,6,8,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[6,7,5,8,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>[6,5,7,8,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[5,6,7,8,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[8,4,1,3,2,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[8,4,1,3,2,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>[7,6,8,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[8,4,1,3,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[6,7,5,8,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>[7,6,5,8,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[5,6,7,8,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[8,4,2,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[3,1,5,2,6,8,7,4]=>[7,8,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[3,1,5,2,7,8,6,4]=>[8,4,2,1,3,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[8,4,2,1,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[7,8,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[8,4,2,1,3,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>[7,5,6,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[6,7,5,8,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[7,6,5,8,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[6,5,7,8,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[5,6,7,8,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[7,8,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[6,7,8,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[7,5,6,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[6,7,5,8,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[7,6,5,8,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[5,6,7,8,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[7,8,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[8,4,3,2,1,5,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[7,6,8,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[6,7,8,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[8,4,3,2,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[7,8,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[8,4,3,2,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[7,5,6,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[7,6,5,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[6,5,7,8,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,6,7,8,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[8,5,1,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[7,8,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[7,6,8,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[6,7,8,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[2,4,6,3,1,7,8,5]=>[8,5,1,2,4,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[2,4,6,3,1,8,7,5]=>[7,8,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[2,4,7,3,1,8,6,5]=>[8,5,1,2,4,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[2,4,8,3,1,6,7,5]=>[6,7,8,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[3,4,2,6,1,7,8,5]=>[8,5,1,3,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[3,4,2,6,1,8,7,5]=>[7,8,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>[6,7,8,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[4,3,6,2,1,7,8,5]=>[8,5,1,4,2,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[4,3,8,2,1,7,6,5]=>[7,6,8,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[6,7,8,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[4,8,2,3,1,7,6,5]=>[7,6,8,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[4,8,2,3,1,6,7,5]=>[6,7,8,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[7,8,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[6,7,8,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[6,7,8,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[8,5,3,1,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[2,4,1,6,3,8,7,5]=>[7,8,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[7,8,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[4,1,2,8,3,7,6,5]=>[7,6,8,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[6,7,8,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[7,8,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[8,5,4,1,2,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[6,7,8,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[7,8,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[7,8,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[7,8,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[7,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[7,8,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[2,3,5,7,4,1,8,6]=>[8,6,1,2,3,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[8,6,1,2,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>[8,6,1,2,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[2,5,7,3,4,1,8,6]=>[8,6,1,2,5,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[3,5,2,8,4,1,7,6]=>[7,8,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[8,6,1,4,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[4,3,5,2,8,1,7,6]=>[7,8,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[4,5,2,3,7,1,8,6]=>[8,6,1,4,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[7,8,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[5,3,4,8,2,1,7,6]=>[7,8,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[5,4,2,7,3,1,8,6]=>[8,6,1,5,3,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[5,7,2,3,4,1,8,6]=>[8,6,1,5,4,3,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[3,1,4,5,8,2,7,6]=>[7,8,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8,6,2,1,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[7,8,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[8,6,2,1,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[7,8,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>[7,8,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[8,6,4,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[7,8,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[8,6,4,1,3,2,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[3,5,2,1,8,4,7,6]=>[7,8,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[7,8,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[7,8,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[8,6,5,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[7,8,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[8,6,5,1,2,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[7,8,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[7,8,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>[7,8,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[4,1,2,8,3,5,7,6]=>[7,8,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>[7,8,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[8,7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[2,6,4,5,8,3,1,7]=>[8,7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[3,4,2,6,8,5,1,7]=>[8,7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[8,7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[8,7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[8,7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>[8,7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>[8,7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>[8,7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[8,7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[2,6,1,5,8,4,3,7]=>[8,7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>[8,7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[8,7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[3,1,6,2,8,5,4,7]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[8,7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[8,7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[8,7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[3,6,2,1,4,8,5,7]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[2,3,5,8,4,1,6,7]=>[8,7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[8,7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[8,7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[3,5,2,8,4,1,6,7]=>[8,7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[8,7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[8,7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[8,7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[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]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[6,5,7,1,2,3,4,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[2,3,6,7,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[5,6,4,7,1,2,3,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[5,4,6,7,1,2,3,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[2,3,7,4,5,6,1,8]=>[4,5,6,7,1,2,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[2,6,5,7,4,3,1,8]=>[7,1,2,6,3,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>[7,1,2,6,5,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[7,1,3,2,5,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[6,7,1,3,2,5,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[5,6,4,7,1,3,2,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[3,7,2,4,5,6,1,8]=>[4,5,6,7,1,3,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[6,7,1,4,3,2,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[6,5,7,1,4,3,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>[7,1,5,4,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[7,1,6,2,5,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[7,1,6,4,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[7,1,6,5,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]=>[6,2,3,4,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>[5,6,2,4,3,7,1,8]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[4,5,3,6,2,7,1,8]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[3,4,5,6,2,7,1,8]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>[5,4,6,3,2,7,1,8]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>[6,4,2,3,5,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[6,5,3,2,4,7,1,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>[4,5,2,3,6,7,1,8]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>[5,6,7,2,1,3,4,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]=>[4,5,6,7,2,1,3,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[7,2,1,4,3,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,1,5,7,4,3,2,8]=>[7,2,1,6,3,5,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[2,6,1,5,7,4,3,8]=>[7,3,1,2,6,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[2,7,1,4,5,6,3,8]=>[4,5,6,7,3,1,2,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>[6,7,3,2,1,4,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>[7,3,2,1,4,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[5,6,4,7,3,2,1,8]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[6,5,4,7,3,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[4,5,6,7,3,2,1,8]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[3,5,2,1,6,7,4,8]=>[7,4,1,3,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[2,5,1,3,6,7,4,8]=>[7,4,3,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[2,6,1,3,7,5,4,8]=>[7,4,3,1,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[6,7,4,3,2,1,5,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[7,4,3,2,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[6,5,7,4,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,6,7,4,3,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[7,5,1,2,3,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[6,7,5,1,2,3,4,8]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>[7,5,1,3,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>[7,5,1,4,2,3,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[7,5,4,1,3,2,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[7,6,1,4,3,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[7,6,5,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>[7,6,5,1,3,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>[7,6,5,1,4,2,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[4,7,2,3,1,5,6,8]=>[7,6,5,1,4,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[3,1,4,7,2,5,6,8]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>[7,6,5,2,1,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[3,7,2,1,4,5,6,8]=>[7,6,5,4,1,3,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[3,4,2,6,5,1,7,8]=>[5,6,1,3,2,4,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[5,4,6,1,3,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[5,6,1,4,2,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>[5,3,2,4,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[5,4,3,2,6,1,7,8]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[5,4,6,2,1,3,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,6,2,1,4,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[6,1,5,3,4,2,7,8]=>[5,4,3,6,2,1,7,8]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[5,4,6,3,1,2,7,8]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[5,6,4,3,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[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]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[4,5,1,2,3,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[4,1,5,3,2,6,7,8]=>[5,2,1,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[3,4,5,2,1,6,7,8]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,5,3,2,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[5,4,1,3,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[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]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
left-to-right-maxima to Dyck path
searching the database
Sorry, this map was not found in the database.