Identifier
Mp00017:
Binary trees
—to 312-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]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[1,3,2]=>[1,0,1,1,0,0]
[[.,[.,.]],.]=>[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]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,2,4,1]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]
[.,[[.,[.,.]],.]]=>[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]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,4,2]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],.]=>[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]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]
[[[.,[.,.]],.],.]=>[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]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,4,3,5,1]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],.]]]=>[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]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2,4,5,1]=>[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,2,5,4,1]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[4,3,2,5,1]=>[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,2,3,5,1]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]
[.,[[.,[.,[.,.]]],.]]=>[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]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]
[.,[[[.,[.,.]],.],.]]=>[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]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,3,5,4,2]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,4,3,5,2]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],.]=>[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]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,2,4,1,5]=>[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]
[[.,[[.,[.,.]],.]],.]=>[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]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,.]]],.],.]=>[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]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[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]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],.]]]]=>[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]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],.]]]=>[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]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[.,[[.,[.,[.,[.,.]]]],.]]=>[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]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[.,[[.,[[.,[.,.]],.]],.]]=>[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]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[.,[.,[.,.]]],.],.]]=>[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]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],.],.],.]]=>[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]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[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]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[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]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[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]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],.],.]],.]=>[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]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[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]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],.]],.],.]=>[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]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],.]=>[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]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[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]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[5,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[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]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[4,7,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[5,4,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[4,5,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[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]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[3,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[3,5,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[4,3,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[3,4,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[5,3,4,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[4,5,3,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[3,5,4,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[4,3,5,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[3,4,5,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[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]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[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]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[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]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[2,4,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[2,5,4,7,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[2,4,5,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[3,2,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[3,2,5,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[2,3,5,7,1,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[4,2,3,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[3,4,2,7,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[2,4,3,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[3,2,4,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[5,2,3,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[4,5,2,3,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[3,5,2,4,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[4,3,5,2,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[3,4,5,2,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[2,5,3,4,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[2,4,5,3,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[3,2,5,4,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[2,3,5,4,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[4,2,3,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[3,4,2,5,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[2,4,3,5,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[3,2,4,5,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[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]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[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]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[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]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[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]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[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]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[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]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[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]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[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]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[1,5,4,7,2,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[1,4,5,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[1,3,5,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[1,4,3,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[1,3,4,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[1,5,3,4,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[1,4,5,3,7,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[1,3,5,4,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[1,4,3,5,7,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[2,1,5,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[2,1,4,7,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[2,1,5,4,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[2,1,4,5,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[1,2,5,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[1,2,4,7,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[1,2,5,4,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[1,2,4,5,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[3,1,2,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[3,4,1,2,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[2,4,1,3,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[3,2,4,1,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[2,3,4,1,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[4,5,1,2,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[3,5,1,2,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[4,3,5,1,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[3,4,5,1,2,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[2,5,1,3,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[2,4,5,1,3,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[3,2,5,1,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[2,3,5,1,4,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[4,2,3,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[2,4,3,5,1,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,4,5,1,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[1,4,5,2,3,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[1,3,5,2,4,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[3,4,1,2,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[2,4,1,3,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[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]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[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]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[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]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[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]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[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]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[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]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[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]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[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]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[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]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[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]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[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]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[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]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[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]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[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]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[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]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[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]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,1]=>[5,8,1,2,3,4,6,7]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]=>[5,7,8,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>[6,5,8,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]=>[5,6,8,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[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]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>[5,7,6,8,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[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]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]=>[4,8,1,2,3,5,6,7]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[2,3,6,5,4,7,8,1]=>[5,4,8,1,2,3,6,7]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>[4,5,8,1,2,3,6,7]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[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]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[2,3,8,6,5,7,4,1]=>[5,7,4,6,8,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[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]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]=>[4,7,5,6,8,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[2,3,8,4,7,6,5,1]=>[4,6,7,5,8,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[2,3,8,5,4,7,6,1]=>[5,4,7,6,8,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[2,3,8,4,5,7,6,1]=>[4,5,7,6,8,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[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]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[2,3,8,4,6,5,7,1]=>[4,6,5,7,8,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[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]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[2,4,3,7,6,5,8,1]=>[3,6,5,8,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>[3,6,7,5,8,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]=>[3,5,6,7,8,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[2,5,4,3,6,8,7,1]=>[4,3,7,8,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[2,5,4,3,7,6,8,1]=>[4,3,6,8,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[2,5,4,3,8,7,6,1]=>[4,3,7,6,8,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>[4,3,6,7,8,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]=>[3,4,8,1,2,5,6,7]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[2,5,3,4,8,7,6,1]=>[3,4,7,6,8,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]=>[3,4,6,7,8,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]=>[4,5,3,7,8,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]=>[6,3,4,5,8,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[2,7,5,4,6,3,8,1]=>[4,6,3,5,8,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>[4,5,3,6,8,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[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]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[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]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[2,8,3,5,6,7,4,1]=>[3,7,4,5,6,8,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[2,8,3,5,7,6,4,1]=>[3,6,7,4,5,8,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[2,8,3,7,6,5,4,1]=>[3,6,5,7,4,8,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>[4,5,3,7,6,8,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]=>[4,3,5,7,6,8,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[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]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[3,2,4,7,6,5,8,1]=>[2,6,5,8,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]=>[2,5,6,7,8,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>[2,4,6,7,8,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[3,2,7,5,6,4,8,1]=>[2,6,4,5,8,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>[2,4,6,5,8,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[3,2,8,5,6,7,4,1]=>[2,7,4,5,6,8,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]=>[2,6,7,4,5,8,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]=>[3,2,8,1,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]=>[3,2,6,8,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[4,3,2,6,5,7,8,1]=>[3,2,5,8,1,4,6,7]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>[3,2,5,6,8,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[4,3,2,8,6,7,5,1]=>[3,2,7,5,6,8,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[4,3,2,8,7,6,5,1]=>[3,2,6,7,5,8,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]=>[3,2,5,6,7,8,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>[2,3,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]=>[2,3,6,5,8,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[4,2,3,8,6,7,5,1]=>[2,3,7,5,6,8,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[4,2,3,8,7,6,5,1]=>[2,3,6,7,5,8,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]=>[2,3,5,6,7,8,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[5,3,4,2,6,7,8,1]=>[4,2,3,8,1,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]=>[4,2,3,6,8,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[3,4,2,8,1,5,6,7]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>[3,4,2,7,8,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[5,4,3,2,7,6,8,1]=>[3,4,2,6,8,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[5,4,3,2,8,6,7,1]=>[3,4,2,6,7,8,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[5,2,4,3,6,7,8,1]=>[2,4,3,8,1,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>[2,4,3,6,8,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>[3,2,4,8,1,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>[2,3,4,8,1,5,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[5,2,3,4,6,8,7,1]=>[2,3,4,7,8,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]=>[2,3,4,6,7,8,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[6,3,4,5,2,7,8,1]=>[5,2,3,4,8,1,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[6,3,4,5,2,8,7,1]=>[5,2,3,4,7,8,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]=>[4,5,6,2,3,8,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]=>[3,5,6,2,4,8,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>[4,3,6,2,5,8,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[7,2,4,5,6,3,8,1]=>[2,6,3,4,5,8,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]=>[3,4,2,6,5,8,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>[2,4,3,6,5,8,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[7,2,3,4,6,5,8,1]=>[2,3,4,6,5,8,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[7,3,4,5,2,6,8,1]=>[5,2,3,4,6,8,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>[2,5,3,4,6,8,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[8,3,4,6,5,7,2,1]=>[5,7,2,3,4,6,8,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[8,3,6,4,5,7,2,1]=>[4,5,7,2,3,6,8,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[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]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[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]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]=>[4,6,3,5,7,2,8,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[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]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[3,5,6,4,7,2,8,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>[3,5,4,6,7,2,8,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[2,4,6,5,7,3,8,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[2,4,5,6,7,3,8,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[2,3,6,7,5,4,8,1]=>[8,2,3,5,7,6,4,1]=>[2,3,6,7,4,5,8,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,2,3,4,6,7,5,1]=>[2,3,4,7,5,6,8,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>[2,3,5,4,7,6,8,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,7,6,1]=>[3,2,4,5,7,6,8,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[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]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[2,5,4,6,3,7,8,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>[3,4,2,6,5,7,8,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[2,4,3,6,5,7,8,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[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]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]=>[1,7,6,8,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[1,3,4,7,6,5,8,2]=>[1,6,5,8,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>[1,6,7,5,8,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>[1,5,6,7,8,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,2]=>[1,4,8,2,3,5,6,7]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>[1,4,6,8,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[1,3,5,4,8,7,6,2]=>[1,4,7,6,8,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]=>[1,4,5,7,8,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>[1,7,4,5,6,8,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[1,3,5,7,8,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]=>[1,3,5,7,6,8,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]=>[1,3,5,6,7,8,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>[1,4,3,8,2,5,6,7]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[1,5,4,3,7,6,8,2]=>[1,4,3,6,8,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[1,4,3,7,6,8,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>[1,3,4,8,2,5,6,7]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[1,5,3,4,7,6,8,2]=>[1,3,4,6,8,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[1,6,4,5,3,8,7,2]=>[1,5,3,4,7,8,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[1,6,5,4,3,7,8,2]=>[1,4,5,3,8,2,6,7]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[1,6,3,5,4,7,8,2]=>[1,3,5,4,8,2,6,7]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[1,7,4,6,5,3,8,2]=>[1,5,6,3,4,8,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]=>[1,5,3,4,6,8,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[1,8,4,5,7,6,3,2]=>[1,6,7,3,4,5,8,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,5,7,6,4,3,8,2]=>[1,8,4,6,5,7,3,2]=>[1,5,7,3,4,6,8,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[1,8,3,6,5,7,4,2]=>[1,3,5,7,4,6,8,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>[1,3,5,4,7,6,8,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>[1,4,3,6,5,7,8,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>[2,1,7,8,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>[2,1,7,6,8,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>[2,1,5,7,8,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>[2,1,6,7,5,8,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]=>[2,1,5,6,7,8,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>[2,1,4,8,3,5,6,7]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>[2,1,4,6,8,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[2,1,6,5,4,7,8,3]=>[2,1,5,4,8,3,6,7]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,3,6,7]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>[2,1,4,6,5,8,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>[2,1,5,7,4,6,8,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,5,6,7,4,8,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>[2,1,4,6,7,5,8,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[2,1,8,5,6,4,7,3]=>[2,1,6,4,5,7,8,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,5,6,4,7,8,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[1,2,4,5,6,8,7,3]=>[1,2,7,8,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>[1,2,6,7,8,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[1,2,4,6,5,7,8,3]=>[1,2,5,8,3,4,6,7]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[1,2,4,6,5,8,7,3]=>[1,2,5,7,8,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>[1,2,6,5,8,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[1,2,4,7,5,6,8,3]=>[1,2,5,6,8,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[1,2,4,8,7,6,5,3]=>[1,2,6,7,5,8,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[1,2,5,6,7,8,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>[1,2,4,8,3,5,6,7]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]=>[1,2,4,7,8,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]=>[1,2,5,4,8,3,6,7]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>[1,2,6,5,4,8,7,3]=>[1,2,5,4,7,8,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[1,2,7,5,6,4,8,3]=>[1,2,6,4,5,8,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]=>[1,2,5,7,4,6,8,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[1,2,5,6,7,4,8,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[3,1,2,8,4,5,6,7]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[2,3,1,5,6,8,7,4]=>[3,1,2,7,8,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[2,3,1,6,5,7,8,4]=>[3,1,2,5,8,4,6,7]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]=>[3,1,2,6,5,8,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[2,3,1,7,5,6,8,4]=>[3,1,2,5,6,8,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>[3,1,2,7,5,6,8,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[3,1,2,6,7,5,8,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[2,3,1,8,5,7,6,4]=>[3,1,2,5,7,6,8,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[3,1,2,5,6,7,8,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,4,5,6,7]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>[2,3,1,7,8,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>[2,3,1,6,8,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>[2,3,1,7,6,8,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>[2,3,1,6,7,8,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>[2,3,1,5,7,6,8,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,3,1,5,6,7,8,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]=>[1,3,2,5,7,8,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]=>[1,3,2,6,5,8,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]=>[1,3,2,7,5,6,8,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[1,3,2,6,5,7,8,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,4,5,6,7]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,8,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>[1,2,3,7,6,8,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>[1,2,3,6,7,8,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,4,6,7]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,8,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>[1,2,3,6,5,8,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>[1,2,3,5,6,8,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>[1,2,3,7,5,6,8,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,6,7,5,8,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[1,2,3,5,7,6,8,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[1,2,3,6,5,7,8,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,7,8,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,6,8,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,7,6,8,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[4,1,2,3,6,7,8,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>[3,4,1,2,8,5,6,7]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>[3,4,1,2,6,8,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[3,4,1,2,7,6,8,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]=>[3,4,1,2,6,7,8,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>[2,4,1,3,8,5,6,7]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>[2,4,1,3,6,8,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[2,4,1,3,7,6,8,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[2,4,1,3,6,7,8,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[3,2,4,1,8,5,6,7]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[3,2,4,1,7,8,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[3,2,4,1,6,8,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[3,2,4,1,6,7,8,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>[2,3,4,1,8,5,6,7]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>[2,3,4,1,7,8,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>[2,3,4,1,6,8,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[2,3,4,1,7,6,8,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,7,6,8,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[1,4,2,3,6,7,8,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,5,6,7]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,8,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,7,6,8,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,8,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,6,8,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,8,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[2,3,1,4,6,8,7,5]=>[3,1,2,4,7,8,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,6,8,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,7,6,8,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,6,7,5]=>[3,1,2,4,6,7,8,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,5,6,7]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,8,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,6,8,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,6,8,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,8,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,8,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,8,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,6,8,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,8,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[2,3,5,4,1,7,8,6]=>[4,5,1,2,3,8,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[3,5,1,2,4,8,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>[3,5,1,2,4,7,8,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>[2,4,5,1,3,7,8,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>[3,2,5,1,4,7,8,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>[2,3,5,1,4,8,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>[4,2,3,5,1,8,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>[3,4,2,5,1,8,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[5,2,4,3,1,7,8,6]=>[2,4,3,5,1,8,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[5,3,2,4,1,7,8,6]=>[3,2,4,5,1,8,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>[1,5,2,3,4,8,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>[1,5,2,3,4,7,8,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>[1,4,5,2,3,8,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[1,4,3,5,2,8,7,6]=>[1,3,5,2,4,7,8,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>[1,4,3,5,2,8,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,4,3,5,2,7,8,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>[1,3,4,5,2,8,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>[1,2,5,3,4,8,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>[1,2,5,3,4,7,8,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[2,4,3,1,5,7,8,6]=>[3,4,1,2,5,8,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[2,4,1,3,5,7,8,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[3,2,4,1,5,8,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>[2,3,4,1,5,8,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>[5,4,6,1,2,3,8,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[3,5,6,1,2,4,8,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>[4,5,3,6,1,2,8,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>[2,4,6,1,3,5,8,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>[2,3,6,1,4,5,8,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[4,2,3,6,5,1,8,7]=>[2,3,5,6,1,4,8,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>[2,4,3,6,1,5,8,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,4,5,2,6,1,8,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>[2,4,5,3,6,1,8,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[6,3,4,2,5,1,8,7]=>[4,2,3,5,6,1,8,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[3,4,2,5,6,1,8,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,3,4,8,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>[2,1,4,6,3,5,8,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[1,2,4,5,6,3,8,7]=>[1,2,6,3,4,5,8,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[2,3,1,5,6,4,8,7]=>[3,1,2,6,4,5,8,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,4,5,8,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[1,3,4,5,2,6,8,7]=>[1,5,2,3,4,6,8,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[2,1,5,3,4,6,8,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[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]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[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]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>[3,5,7,1,2,4,6,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[2,6,5,4,3,7,1,8]=>[4,5,3,7,1,2,6,8]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[2,4,6,7,1,3,5,8]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>[3,4,2,7,1,5,6,8]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]=>[2,3,4,7,1,5,6,8]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>[4,5,2,3,7,1,6,8]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[6,4,3,5,2,7,1,8]=>[3,5,2,4,7,1,6,8]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]=>[3,2,5,4,7,1,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[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]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[7,4,3,5,6,2,1,8]=>[3,6,2,4,5,7,1,8]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[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]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[3,5,4,6,2,7,1,8]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[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]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>[2,5,4,6,3,7,1,8]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>[3,4,2,6,5,7,1,8]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>[2,4,3,6,5,7,1,8]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[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]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>[2,5,3,4,6,7,1,8]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[1,3,6,4,5,7,2,8]=>[1,4,5,7,2,3,6,8]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[1,3,7,4,6,5,2,8]=>[1,4,6,5,7,2,3,8]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>[1,3,5,7,2,4,6,8]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[1,4,3,7,5,6,2,8]=>[1,3,5,6,7,2,4,8]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[1,6,5,4,3,7,2,8]=>[1,4,5,3,7,2,6,8]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[1,7,4,3,6,5,2,8]=>[1,4,3,6,5,7,2,8]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]=>[1,2,7,3,4,5,6,8]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>[1,2,5,6,4,7,3,8]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]=>[3,1,2,5,7,4,6,8]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>[2,3,1,6,5,7,4,8]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,4,5,6,8]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,7,4,5,8]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>[1,3,2,5,7,4,6,8]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>[1,3,2,6,5,7,4,8]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]=>[1,3,2,5,6,7,4,8]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,4,5,6,8]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,7,4,5,8]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]=>[1,2,3,5,7,4,6,8]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[1,2,3,6,5,7,4,8]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,2,3,5,6,7,4,8]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[3,2,4,1,7,5,6,8]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[3,2,4,1,6,7,5,8]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[4,2,3,1,6,7,5,8]=>[2,3,4,1,7,5,6,8]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,1,2,4,7,5,6,8]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,5,6,8]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]=>[4,5,1,2,3,7,6,8]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>[3,5,1,2,4,7,6,8]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[2,5,4,3,1,7,6,8]=>[4,3,5,1,2,7,6,8]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[4,2,3,5,1,7,6,8]=>[2,3,5,1,4,7,6,8]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[3,4,2,5,1,7,6,8]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[1,3,5,2,4,7,6,8]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[3,2,6,4,5,1,7,8]=>[2,4,5,6,1,3,7,8]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[1,3,6,5,4,2,7,8]=>[1,5,4,6,2,3,7,8]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>[1,3,5,6,2,4,7,8]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>[1,4,3,6,2,5,7,8]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>[2,1,5,6,3,4,7,8]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>[1,2,6,3,4,5,7,8]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>[1,2,5,6,3,4,7,8]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[1,2,4,5,6,3,7,8]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,4,5,7,8]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,4,5,7,8]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[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]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[3,5,1,2,4,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[2,5,1,3,4,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[3,2,5,1,4,6,7,8]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[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]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[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]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[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]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[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]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[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]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[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 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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 maxima 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 weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak 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.