Identifier
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1
[.,.]=>[1,0]=>[1]=>[1]
[.,[.,.]]=>[1,0,1,0]=>[1,2]=>[2,1]
[[.,.],.]=>[1,1,0,0]=>[2,1]=>[1,2]
[.,[.,[.,.]]]=>[1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]
[.,[[.,.],.]]=>[1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]
[[.,.],[.,.]]=>[1,1,0,0,1,0]=>[2,1,3]=>[2,3,1]
[[.,[.,.]],.]=>[1,1,0,1,0,0]=>[2,3,1]=>[2,1,3]
[[[.,.],.],.]=>[1,1,1,0,0,0]=>[3,1,2]=>[1,3,2]
[.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]
[.,[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,3,1,2]
[.,[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]
[.,[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[4,2,1,3]
[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>[4,1,3,2]
[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[3,4,2,1]
[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]
[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,4,1]
[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>[2,4,3,1]
[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[3,2,1,4]
[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>[2,4,1,3]=>[3,1,4,2]
[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>[3,1,4,2]=>[2,4,1,3]
[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>[3,4,1,2]=>[2,1,4,3]
[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>[1,4,3,2]
[.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]
[.,[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,4,3,1,2]
[.,[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,4,2,3,1]
[.,[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[5,4,2,1,3]
[.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>[5,4,1,3,2]
[.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,3,4,2,1]
[.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[5,3,4,1,2]
[.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,3,2,4,1]
[.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>[5,2,4,3,1]
[.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[5,3,2,1,4]
[.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[5,3,1,4,2]
[.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>[5,2,4,1,3]
[.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>[5,2,1,4,3]
[.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>[5,1,4,3,2]
[[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[4,5,3,2,1]
[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]
[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[4,5,2,3,1]
[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,5,2,1,3]
[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>[4,5,1,3,2]
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[4,3,5,2,1]
[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,3,5,1,2]
[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>[3,5,4,2,1]
[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>[3,5,4,1,2]
[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,3,2,5,1]
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>[4,2,5,3,1]
[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>[3,5,2,4,1]
[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>[3,2,5,4,1]
[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>[2,5,4,3,1]
[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]
[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[4,3,1,5,2]
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]
[[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>[4,2,1,5,3]
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>[4,1,5,3,2]
[[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>[3,5,2,1,4]
[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>[3,5,1,4,2]
[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>[3,2,5,1,4]
[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>[2,5,4,1,3]
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>[3,2,1,5,4]
[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>[3,1,5,4,2]
[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>[2,5,1,4,3]
[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>[2,1,5,4,3]
[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>[1,5,4,3,2]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]
[.,[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]
[.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]
[.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]
[.,[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]
[.,[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]
[.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]
[.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]
[.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]
[.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]
[.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]
[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]
[.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]
[.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]
[.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]
[.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]
[.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]
[.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]
[.,[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]
[.,[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]
[.,[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]
[.,[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]
[.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]
[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]
[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]
[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]
[[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]
[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]
[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]
[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]
[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]
[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]
[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]
[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]
[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]
[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]
[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]
[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]
[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]
[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]
[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]
[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]
[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]
[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]
[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>[4,3,6,2,1,5]
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]
[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]
[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>[4,3,2,6,1,5]
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]
[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>[3,2,6,5,1,4]
[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]
[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]
[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>[3,6,2,1,5,4]
[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]
[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>[2,6,5,1,4,3]
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]
[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]
[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>[2,6,1,5,4,3]
[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]
[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[8,7,6,4,3,5,1,2]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[8,7,6,2,1,5,4,3]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,5,6,8]=>[8,7,5,6,2,4,3,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[8,7,5,4,6,2,1,3]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>[8,7,5,4,3,6,1,2]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,3,4,5,8,7]=>[8,7,3,6,5,4,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,3,4,8]=>[8,7,4,3,2,6,5,1]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,3,4,5,8]=>[8,7,3,2,6,5,4,1]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,3,7,8,5]=>[8,7,5,3,6,2,1,4]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,3,8,5,7]=>[8,7,5,3,6,1,4,2]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,3,5,8,6]=>[8,7,5,2,6,4,1,3]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,3,8,5,6]=>[8,7,5,2,6,1,4,3]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,3,6,8,4,7]=>[8,7,4,6,3,1,5,2]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>[8,7,4,3,1,6,5,2]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[8,6,7,5,3,4,1,2]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[8,6,7,5,2,4,1,3]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[8,6,7,4,3,5,1,2]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,4,5,8,7]=>[8,6,7,3,5,4,1,2]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,4,5,8]=>[8,6,7,3,2,5,4,1]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,4,8,5]=>[8,6,7,3,2,5,1,4]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[8,6,7,2,5,4,1,3]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,4,5]=>[8,6,7,3,2,1,5,4]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,4,5,7]=>[8,6,7,3,1,5,4,2]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,4,5,6]=>[8,6,7,2,1,5,4,3]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,5,7,8]=>[8,6,5,7,3,4,2,1]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,5,7]=>[8,6,5,7,3,1,4,2]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>[8,6,5,7,2,1,4,3]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,3,6,5,7,8]=>[8,5,7,6,3,4,2,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[8,5,7,6,2,4,1,3]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>[8,6,5,4,7,3,1,2]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[8,6,5,4,7,2,1,3]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,6,7]=>[8,6,5,4,7,1,3,2]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,3,6,8,7]=>[8,5,7,4,6,3,1,2]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,2,3,7,6,8]=>[8,5,4,7,6,2,3,1]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[8,5,4,7,6,1,3,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>[8,6,5,4,3,7,1,2]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,4,6,2,5,7,8]=>[8,6,5,3,7,4,2,1]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,2,5,8,7]=>[8,6,5,3,7,4,1,2]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,2,4,5,7,8]=>[8,6,3,7,5,4,2,1]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,2,4,5,8,7]=>[8,6,3,7,5,4,1,2]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,2,3,5,7,8]=>[8,5,3,7,6,4,2,1]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,5,8,7]=>[8,3,7,6,5,4,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,2,5,8]=>[8,6,5,3,2,7,4,1]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,2,7,4,5,8]=>[8,6,3,7,2,5,4,1]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,2,6,7,3,5,8]=>[8,5,7,3,2,6,4,1]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,7,3,8]=>[8,5,4,7,3,2,6,1]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,2,3,6,7,4,8]=>[8,4,7,6,3,2,5,1]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,5,6,2,3,7,4,8]=>[8,4,3,7,6,2,5,1]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,2,3,5,6,8]=>[8,5,2,7,6,4,3,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,2,6,7,3,4,8]=>[8,4,7,3,2,6,5,1]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,2,7,3,4,8]=>[8,4,3,7,2,6,5,1]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[8,6,5,4,3,2,1,7]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,2,8,6]=>[8,6,5,4,2,7,1,3]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,2,6]=>[8,6,5,4,2,1,7,3]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>[8,6,5,4,1,7,3,2]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,2,7,8,5]=>[8,6,5,3,7,2,1,4]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,2,8,5]=>[8,6,5,3,2,7,1,4]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,2,5,8,6]=>[8,6,5,2,7,4,1,3]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>[8,6,5,3,1,7,4,2]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,2,6,7,8,4]=>[8,6,4,7,3,2,1,5]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,2,7,8,4]=>[8,6,4,3,7,2,1,5]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,2,4,7]=>[8,6,4,3,1,7,5,2]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[8,6,2,1,7,5,4,3]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]=>[8,5,7,3,6,2,1,4]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[8,5,7,2,6,4,1,3]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[8,5,4,7,3,1,6,2]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>[8,5,4,7,2,1,6,3]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,2,3,8,4,6,7]=>[8,4,7,6,1,5,3,2]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,2,8,3,7]=>[8,5,4,3,7,1,6,2]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,2,3,7,8,5]=>[8,5,3,7,6,2,1,4]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>[8,3,7,6,5,2,1,4]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,2,3,5,8,6]=>[8,5,2,7,6,4,1,3]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,7,2,8,3,6]=>[8,5,4,2,7,1,6,3]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,2,8,3,5]=>[8,5,3,2,7,1,6,4]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[8,5,3,1,7,6,4,2]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,2,6,7,8,3,4]=>[8,4,7,3,2,1,6,5]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[7,8,6,5,4,2,1,3]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[7,8,6,5,3,4,2,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[7,8,6,5,3,4,1,2]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>[7,8,6,5,3,2,4,1]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>[7,8,6,5,2,4,3,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[7,8,6,5,3,2,1,4]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,4,6,8,5,7]=>[7,8,6,5,3,1,4,2]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,5,8,6]=>[7,8,6,5,2,4,1,3]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,5,6]=>[7,8,6,5,2,1,4,3]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>[7,8,6,5,1,4,3,2]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[7,8,6,4,5,3,2,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[7,8,6,4,5,2,1,3]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,6,7]=>[7,8,6,4,5,1,3,2]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[7,8,6,4,3,5,1,2]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,4,5,7,8]=>[7,8,6,3,5,4,2,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,4,5,8,7]=>[7,8,6,3,5,4,1,2]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,6,7,4,8]=>[7,8,6,4,3,2,5,1]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6,8]=>[7,8,6,4,2,5,3,1]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5,8]=>[7,8,6,3,5,2,4,1]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,5,8]=>[7,8,6,3,2,5,4,1]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,7,4,5,6,8]=>[7,8,6,2,5,4,3,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[7,8,6,4,3,2,1,5]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,3,5,6,8,4,7]=>[7,8,6,4,3,1,5,2]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,4,8,6]=>[7,8,6,4,2,5,1,3]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,4,6]=>[7,8,6,4,2,1,5,3]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,3,5,8,4,6,7]=>[7,8,6,4,1,5,3,2]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,6,4,7,8,5]=>[7,8,6,3,5,2,1,4]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,4,8,5,7]=>[7,8,6,3,5,1,4,2]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,4,8,5]=>[7,8,6,3,2,5,1,4]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,4,5]=>[7,8,6,3,2,1,5,4]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,4,5,7]=>[7,8,6,3,1,5,4,2]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,7,4,8,5,6]=>[7,8,6,2,5,1,4,3]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,4,5,6]=>[7,8,6,2,1,5,4,3]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[7,8,6,1,5,4,3,2]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[7,8,5,6,4,3,2,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[7,8,5,6,4,3,1,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[7,8,5,6,4,2,1,3]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[7,8,5,6,3,4,2,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>[7,8,5,6,3,2,4,1]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,7,5,6,8]=>[7,8,5,6,2,4,3,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[7,8,5,6,3,2,1,4]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7]=>[7,8,5,6,3,1,4,2]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,8,6]=>[7,8,5,6,2,4,1,3]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>[7,8,5,6,1,4,3,2]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[7,8,5,4,6,3,2,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[7,8,5,4,6,3,1,2]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[7,8,4,6,5,3,2,1]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,3,4,6,8,7]=>[7,8,4,6,5,3,1,2]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,3,4,7,6,8]=>[7,8,4,6,5,2,3,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,6,3,7,8]=>[7,8,5,4,3,6,2,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[7,8,5,4,3,6,1,2]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,3,5,7,8]=>[7,8,5,3,6,4,2,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,4,7,8]=>[7,8,4,6,3,5,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,3,4,7,8]=>[7,8,4,3,6,5,2,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7,8]=>[7,8,3,6,5,4,2,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>[7,8,3,6,5,4,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[7,8,5,4,3,2,6,1]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,5,8]=>[7,8,5,3,2,6,4,1]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,7,3,5,6,8]=>[7,8,5,2,6,4,3,1]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,3,6,7,4,8]=>[7,8,4,6,3,2,5,1]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,7,4,6,8]=>[7,8,4,6,2,5,3,1]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>[7,8,4,3,6,2,5,1]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,6,3,4,7,5,8]=>[7,8,3,6,5,2,4,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>[7,8,4,3,2,6,5,1]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>[7,8,4,2,6,5,3,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,7,4,5,8]=>[7,8,3,6,2,5,4,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,3,4,5,8]=>[7,8,3,2,6,5,4,1]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,3,4,5,6,8]=>[7,8,2,6,5,4,3,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[7,8,5,4,3,2,1,6]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,3,7]=>[7,8,5,4,3,1,6,2]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,3,8,6]=>[7,8,5,4,2,6,1,3]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,3,6]=>[7,8,5,4,2,1,6,3]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,3,6,7]=>[7,8,5,4,1,6,3,2]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,3,7,8,5]=>[7,8,5,3,6,2,1,4]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,3,8,5,7]=>[7,8,5,3,6,1,4,2]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,3,8,5]=>[7,8,5,3,2,6,1,4]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,3,5,8,6]=>[7,8,5,2,6,4,1,3]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,3,5]=>[7,8,5,3,2,1,6,4]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,3,5,7]=>[7,8,5,3,1,6,4,2]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,3,8,5,6]=>[7,8,5,2,6,1,4,3]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,3,5,6]=>[7,8,5,2,1,6,4,3]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[7,8,5,1,6,4,3,2]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,3,6,7,8,4]=>[7,8,4,6,3,2,1,5]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,3,6,8,4,7]=>[7,8,4,6,3,1,5,2]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>[7,8,4,6,2,5,1,3]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,3,7,8,4,6]=>[7,8,4,6,2,1,5,3]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,8,4,6,7]=>[7,8,4,6,1,5,3,2]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,7,8,4]=>[7,8,4,3,6,2,1,5]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,3,8,4,7]=>[7,8,4,3,6,1,5,2]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,3,4,7,8,5]=>[7,8,3,6,5,2,1,4]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,3,4,8,5,7]=>[7,8,3,6,5,1,4,2]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,3,8,4]=>[7,8,4,3,2,6,1,5]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,3,4,8,6]=>[7,8,4,2,6,5,1,3]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>[7,8,3,6,2,5,1,4]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,3,4,8,5]=>[7,8,3,2,6,5,1,4]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,3,4,5,8,6]=>[7,8,2,6,5,4,1,3]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,3,4]=>[7,8,4,3,2,1,6,5]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,3,4,7]=>[7,8,4,3,1,6,5,2]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,3,4,6]=>[7,8,4,2,1,6,5,3]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,3,4,6,7]=>[7,8,4,1,6,5,3,2]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,3,7,8,4,5]=>[7,8,3,6,2,1,5,4]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,8,4,5,7]=>[7,8,3,6,1,5,4,2]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,3,8,4,5]=>[7,8,3,2,6,1,5,4]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,3,4,8,5,6]=>[7,8,2,6,5,1,4,3]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,3,4,5,7]=>[7,8,3,1,6,5,4,2]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,8,4,5,6]=>[7,8,2,6,1,5,4,3]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[7,8,2,1,6,5,4,3]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[7,8,1,6,5,4,3,2]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[7,6,8,5,4,2,1,3]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5,8,6,7]=>[7,6,8,5,4,1,3,2]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,4,6,5,7,8]=>[7,6,8,5,3,4,2,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>[7,6,8,5,3,4,1,2]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[7,6,8,5,3,2,4,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[7,6,8,5,3,2,1,4]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,1,4,6,8,5,7]=>[7,6,8,5,3,1,4,2]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,5,8,6]=>[7,6,8,5,2,4,1,3]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,5,6]=>[7,6,8,5,2,1,4,3]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,5,6,7]=>[7,6,8,5,1,4,3,2]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[7,6,8,4,5,3,2,1]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,4,6,8,7]=>[7,6,8,4,5,3,1,2]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[7,6,8,4,5,2,3,1]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[7,6,8,4,3,5,2,1]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7]=>[7,6,8,4,3,5,1,2]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,4,5,7,8]=>[7,6,8,3,5,4,2,1]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,4,5,8,7]=>[7,6,8,3,5,4,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[7,6,8,4,3,2,5,1]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,1,5,7,4,6,8]=>[7,6,8,4,2,5,3,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5,8]=>[7,6,8,3,5,2,4,1]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,4,5,8]=>[7,6,8,3,2,5,4,1]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,7,4,5,6,8]=>[7,6,8,2,5,4,3,1]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[7,6,8,4,3,2,1,5]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,4,7]=>[7,6,8,4,3,1,5,2]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,8,6]=>[7,6,8,4,2,5,1,3]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,4,6]=>[7,6,8,4,2,1,5,3]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,1,5,8,4,6,7]=>[7,6,8,4,1,5,3,2]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]=>[7,6,8,3,5,2,1,4]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,8,5,7]=>[7,6,8,3,5,1,4,2]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]=>[7,6,8,3,2,5,1,4]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[7,6,8,2,5,4,1,3]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,4,5]=>[7,6,8,3,2,1,5,4]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,4,5,7]=>[7,6,8,3,1,5,4,2]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,8,5,6]=>[7,6,8,2,5,1,4,3]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,4,5,6]=>[7,6,8,2,1,5,4,3]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[7,6,8,1,5,4,3,2]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,6,8,7]=>[6,8,7,5,4,3,1,2]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,5,7,8,6]=>[6,8,7,5,4,2,1,3]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>[6,8,7,5,4,1,3,2]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,4,6,5,7,8]=>[6,8,7,5,3,4,2,1]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,4,6,5,8,7]=>[6,8,7,5,3,4,1,2]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>[6,8,7,5,3,2,4,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[6,8,7,5,2,4,3,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,4,6,7,8,5]=>[6,8,7,5,3,2,1,4]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,4,6,8,5,7]=>[6,8,7,5,3,1,4,2]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,4,7,5,8,6]=>[6,8,7,5,2,4,1,3]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,2,4,7,8,5,6]=>[6,8,7,5,2,1,4,3]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>[6,8,7,5,1,4,3,2]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,2,5,4,6,7,8]=>[6,8,7,4,5,3,2,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,5,4,6,8,7]=>[6,8,7,4,5,3,1,2]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[6,8,7,4,5,2,3,1]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,2,5,4,7,8,6]=>[6,8,7,4,5,2,1,3]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,8,6,7]=>[6,8,7,4,5,1,3,2]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,2,5,6,4,7,8]=>[6,8,7,4,3,5,2,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,2,5,6,4,8,7]=>[6,8,7,4,3,5,1,2]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,2,6,4,5,7,8]=>[6,8,7,3,5,4,2,1]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,2,6,4,5,8,7]=>[6,8,7,3,5,4,1,2]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>[6,8,7,4,3,2,5,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[6,8,7,4,2,5,3,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>[6,8,7,3,5,2,4,1]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,5,8]=>[6,8,7,3,2,5,4,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,8,4]=>[6,8,7,4,3,2,1,5]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,2,5,6,8,4,7]=>[6,8,7,4,3,1,5,2]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,5,7,4,8,6]=>[6,8,7,4,2,5,1,3]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,2,5,7,8,4,6]=>[6,8,7,4,2,1,5,3]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,5,8,4,6,7]=>[6,8,7,4,1,5,3,2]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,2,6,4,7,8,5]=>[6,8,7,3,5,2,1,4]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,2,6,4,8,5,7]=>[6,8,7,3,5,1,4,2]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,6,7,4,8,5]=>[6,8,7,3,2,5,1,4]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,2,7,4,5,8,6]=>[6,8,7,2,5,4,1,3]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,2,6,7,8,4,5]=>[6,8,7,3,2,1,5,4]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,2,6,8,4,5,7]=>[6,8,7,3,1,5,4,2]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,2,7,4,8,5,6]=>[6,8,7,2,5,1,4,3]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,2,7,8,4,5,6]=>[6,8,7,2,1,5,4,3]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[6,8,7,1,5,4,3,2]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[7,6,5,8,4,3,1,2]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[7,6,5,8,4,2,3,1]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[7,6,5,8,4,2,1,3]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[7,6,5,8,4,1,3,2]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[7,6,5,8,3,4,2,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[7,6,5,8,3,4,1,2]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[7,6,5,8,3,2,4,1]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,5,6,8]=>[7,6,5,8,2,4,3,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[7,6,5,8,3,2,1,4]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>[7,6,5,8,3,1,4,2]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,8,6]=>[7,6,5,8,2,4,1,3]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[7,6,5,8,2,1,4,3]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7,8]=>[7,5,8,6,4,3,2,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5,6,8,7]=>[7,5,8,6,4,3,1,2]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,3,5,7,6,8]=>[7,5,8,6,4,2,3,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,3,5,7,8,6]=>[7,5,8,6,4,2,1,3]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,3,5,8,6,7]=>[7,5,8,6,4,1,3,2]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,3,6,5,7,8]=>[7,5,8,6,3,4,2,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[7,5,8,6,3,4,1,2]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,3,6,7,5,8]=>[7,5,8,6,3,2,4,1]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,3,7,5,6,8]=>[7,5,8,6,2,4,3,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,3,6,7,8,5]=>[7,5,8,6,3,2,1,4]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,3,7,5,8,6]=>[7,5,8,6,2,4,1,3]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,3,7,8,5,6]=>[7,5,8,6,2,1,4,3]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,3,8,5,6,7]=>[7,5,8,6,1,4,3,2]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[6,8,5,7,4,3,2,1]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,2,5,6,8,7]=>[6,8,5,7,4,3,1,2]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,2,5,7,6,8]=>[6,8,5,7,4,2,3,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,2,5,7,8,6]=>[6,8,5,7,4,2,1,3]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,2,5,8,6,7]=>[6,8,5,7,4,1,3,2]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[6,8,5,7,3,4,2,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>[6,8,5,7,3,4,1,2]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,2,6,7,5,8]=>[6,8,5,7,3,2,4,1]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,7,5,6,8]=>[6,8,5,7,2,4,3,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,2,6,7,8,5]=>[6,8,5,7,3,2,1,4]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,2,6,8,5,7]=>[6,8,5,7,3,1,4,2]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,2,7,8,5,6]=>[6,8,5,7,2,1,4,3]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,8,5,6,7]=>[6,8,5,7,1,4,3,2]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>[6,5,8,7,4,3,1,2]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,2,5,7,6,8]=>[6,5,8,7,4,2,3,1]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,2,5,7,8,6]=>[6,5,8,7,4,2,1,3]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,2,5,8,6,7]=>[6,5,8,7,4,1,3,2]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,2,6,5,7,8]=>[6,5,8,7,3,4,2,1]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,2,6,7,5,8]=>[6,5,8,7,3,2,4,1]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,2,7,5,6,8]=>[6,5,8,7,2,4,3,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,2,6,7,8,5]=>[6,5,8,7,3,2,1,4]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,2,6,8,5,7]=>[6,5,8,7,3,1,4,2]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,2,7,5,8,6]=>[6,5,8,7,2,4,1,3]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,2,8,5,6,7]=>[6,5,8,7,1,4,3,2]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,3,5,6,8,7]=>[5,8,7,6,4,3,1,2]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[5,8,7,6,4,2,3,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,3,5,7,8,6]=>[5,8,7,6,4,2,1,3]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>[5,8,7,6,4,1,3,2]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>[5,8,7,6,3,4,2,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>[5,8,7,6,3,4,1,2]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[5,8,7,6,3,2,4,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[5,8,7,6,2,4,3,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,3,6,7,8,5]=>[5,8,7,6,3,2,1,4]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,3,6,8,5,7]=>[5,8,7,6,3,1,4,2]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,3,7,5,8,6]=>[5,8,7,6,2,4,1,3]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,3,7,8,5,6]=>[5,8,7,6,2,1,4,3]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>[5,8,7,6,1,4,3,2]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[7,6,5,4,8,3,1,2]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[7,6,5,4,8,2,3,1]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[7,6,5,4,8,2,1,3]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,6,7]=>[7,6,5,4,8,1,3,2]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,1,4,6,7,8]=>[7,6,4,8,5,3,2,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,1,4,6,8,7]=>[7,6,4,8,5,3,1,2]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,4,7,6,8]=>[7,6,4,8,5,2,3,1]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,5,1,4,7,8,6]=>[7,6,4,8,5,2,1,3]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[7,6,4,8,5,1,3,2]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,3,6,7,8]=>[7,5,8,4,6,3,2,1]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,3,6,8,7]=>[7,5,8,4,6,3,1,2]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,8]=>[7,5,8,4,6,2,3,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[7,5,8,4,6,2,1,3]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,8,6,7]=>[7,5,8,4,6,1,3,2]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,1,3,6,7,8]=>[7,5,4,8,6,3,2,1]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,1,3,6,8,7]=>[7,5,4,8,6,3,1,2]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,1,3,7,6,8]=>[7,5,4,8,6,2,3,1]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,1,3,7,8,6]=>[7,5,4,8,6,2,1,3]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,1,3,8,6,7]=>[7,5,4,8,6,1,3,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,4,6,7,8]=>[7,4,8,6,5,3,2,1]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,4,6,8,7]=>[7,4,8,6,5,3,1,2]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,1,3,4,7,6,8]=>[7,4,8,6,5,2,3,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,4,7,8,6]=>[7,4,8,6,5,2,1,3]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,4,8,6,7]=>[7,4,8,6,5,1,3,2]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,2,6,7,8]=>[6,8,5,4,7,3,2,1]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6,8,7]=>[6,8,5,4,7,3,1,2]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[6,8,5,4,7,2,3,1]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,5,2,7,8,6]=>[6,8,5,4,7,2,1,3]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,5,2,8,6,7]=>[6,8,5,4,7,1,3,2]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]=>[6,8,4,7,5,3,2,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,5,2,4,6,8,7]=>[6,8,4,7,5,3,1,2]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,8]=>[6,8,4,7,5,2,3,1]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,5,2,4,7,8,6]=>[6,8,4,7,5,2,1,3]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,5,2,4,8,6,7]=>[6,8,4,7,5,1,3,2]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,2,6,7,8]=>[6,5,8,4,7,3,2,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,2,6,8,7]=>[6,5,8,4,7,3,1,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6,8]=>[6,5,8,4,7,2,3,1]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]=>[6,5,8,4,7,2,1,3]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,8,6,7]=>[6,5,8,4,7,1,3,2]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,2,5,3,6,7,8]=>[5,8,7,4,6,3,2,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[5,8,7,4,6,2,3,1]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,5,3,7,8,6]=>[5,8,7,4,6,2,1,3]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,8,6,7]=>[5,8,7,4,6,1,3,2]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,1,2,6,8,7]=>[6,5,4,8,7,3,1,2]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,1,2,7,6,8]=>[6,5,4,8,7,2,3,1]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,1,2,7,8,6]=>[6,5,4,8,7,2,1,3]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[6,5,4,8,7,1,3,2]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,4,6,7,8]=>[6,4,8,7,5,3,2,1]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[6,4,8,7,5,3,1,2]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,4,7,6,8]=>[6,4,8,7,5,2,3,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,4,7,8,6]=>[6,4,8,7,5,2,1,3]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,4,8,6,7]=>[6,4,8,7,5,1,3,2]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[5,8,4,7,6,3,2,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,5,2,3,6,8,7]=>[5,8,4,7,6,3,1,2]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,2,3,7,6,8]=>[5,8,4,7,6,2,3,1]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,5,2,3,7,8,6]=>[5,8,4,7,6,2,1,3]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,5,2,3,8,6,7]=>[5,8,4,7,6,1,3,2]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,3,6,7,8]=>[5,4,8,7,6,3,2,1]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[5,4,8,7,6,3,1,2]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,3,7,6,8]=>[5,4,8,7,6,2,3,1]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,3,7,8,6]=>[5,4,8,7,6,2,1,3]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,3,8,6,7]=>[5,4,8,7,6,1,3,2]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,4,6,8,7]=>[4,8,7,6,5,3,1,2]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,3,4,7,6,8]=>[4,8,7,6,5,2,3,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,4,7,8,6]=>[4,8,7,6,5,2,1,3]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,4,8,6,7]=>[4,8,7,6,5,1,3,2]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[7,6,5,4,3,8,1,2]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,1,5,7,8]=>[7,6,5,3,8,4,2,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,4,6,1,5,8,7]=>[7,6,5,3,8,4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,4,7,8]=>[7,6,4,8,3,5,2,1]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,8,7]=>[7,6,4,8,3,5,1,2]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,1,4,7,8]=>[7,6,4,3,8,5,2,1]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,1,4,8,7]=>[7,6,4,3,8,5,1,2]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,1,4,5,7,8]=>[7,6,3,8,5,4,2,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,1,4,5,8,7]=>[7,6,3,8,5,4,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3,7,8]=>[7,5,8,4,3,6,2,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,6,3,8,7]=>[7,5,8,4,3,6,1,2]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,6,3,5,7,8]=>[7,5,8,3,6,4,2,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7]=>[7,5,8,3,6,4,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,3,7,8]=>[7,5,4,8,3,6,2,1]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,5,1,3,6,4,7,8]=>[7,4,8,6,3,5,2,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]=>[7,4,8,6,3,5,1,2]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,1,3,7,8]=>[7,5,4,3,8,6,2,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,6,1,3,8,7]=>[7,5,4,3,8,6,1,2]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,1,3,5,7,8]=>[7,5,3,8,6,4,2,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,1,3,5,8,7]=>[7,5,3,8,6,4,1,2]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,1,6,3,4,7,8]=>[7,4,8,3,6,5,2,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,5,1,6,3,4,8,7]=>[7,4,8,3,6,5,1,2]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,5,6,1,3,4,7,8]=>[7,4,3,8,6,5,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,1,3,4,8,7]=>[7,4,3,8,6,5,1,2]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,6,1,3,4,5,7,8]=>[7,3,8,6,5,4,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>[7,3,8,6,5,4,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,6,2,7,8]=>[6,8,5,4,3,7,2,1]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,6,2,8,7]=>[6,8,5,4,3,7,1,2]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,6,2,5,7,8]=>[6,8,5,3,7,4,2,1]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,5,8,7]=>[6,8,5,3,7,4,1,2]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]=>[6,8,4,7,3,5,2,1]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>[6,8,4,7,3,5,1,2]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,5,6,2,4,7,8]=>[6,8,4,3,7,5,2,1]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,5,6,2,4,8,7]=>[6,8,4,3,7,5,1,2]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[6,8,3,7,5,4,2,1]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,6,2,4,5,8,7]=>[6,8,3,7,5,4,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2,7,8]=>[6,5,8,4,3,7,2,1]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,6,2,8,7]=>[6,5,8,4,3,7,1,2]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,6,2,5,7,8]=>[6,5,8,3,7,4,2,1]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,6,2,5,8,7]=>[6,5,8,3,7,4,1,2]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,2,5,6,3,7,8]=>[5,8,7,4,3,6,2,1]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,5,6,3,8,7]=>[5,8,7,4,3,6,1,2]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,2,6,3,5,7,8]=>[5,8,7,3,6,4,2,1]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,2,6,3,5,8,7]=>[5,8,7,3,6,4,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,2,7,8]=>[6,5,4,8,3,7,2,1]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,8,7]=>[6,5,4,8,3,7,1,2]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,1,2,6,4,7,8]=>[6,4,8,7,3,5,2,1]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]=>[6,4,8,7,3,5,1,2]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[5,8,4,7,3,6,2,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7]=>[5,8,4,7,3,6,1,2]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,1,2,6,3,7,8]=>[5,4,8,7,3,6,2,1]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[5,4,8,7,3,6,1,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,3,6,4,7,8]=>[4,8,7,6,3,5,2,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,3,6,4,8,7]=>[4,8,7,6,3,5,1,2]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,1,2,8,7]=>[6,5,4,3,8,7,1,2]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,4,6,1,2,5,7,8]=>[6,5,3,8,7,4,2,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,1,2,5,8,7]=>[6,5,3,8,7,4,1,2]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,1,6,2,4,7,8]=>[6,4,8,3,7,5,2,1]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,5,6,1,2,4,7,8]=>[6,4,3,8,7,5,2,1]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,1,2,4,8,7]=>[6,4,3,8,7,5,1,2]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,5,7,8]=>[6,3,8,7,5,4,2,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,8,7]=>[6,3,8,7,5,4,1,2]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,6,2,3,7,8]=>[5,8,4,3,7,6,2,1]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,5,6,2,3,8,7]=>[5,8,4,3,7,6,1,2]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[5,8,3,7,6,4,2,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,6,2,3,5,8,7]=>[5,8,3,7,6,4,1,2]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,1,6,2,3,7,8]=>[5,4,8,3,7,6,2,1]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,1,6,2,3,8,7]=>[5,4,8,3,7,6,1,2]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,2,6,3,4,7,8]=>[4,8,7,3,6,5,2,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2,6,3,4,8,7]=>[4,8,7,3,6,5,1,2]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,6,1,2,3,5,7,8]=>[5,3,8,7,6,4,2,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[5,3,8,7,6,4,1,2]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>[4,8,3,7,6,5,2,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,6,2,3,4,8,7]=>[4,8,3,7,6,5,1,2]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,8,7]=>[4,3,8,7,6,5,1,2]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7]=>[3,8,7,6,5,4,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,1,6,8]=>[7,6,5,4,2,8,3,1]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,1,7,5,8]=>[7,6,5,3,8,2,4,1]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,1,5,8]=>[7,6,5,3,2,8,4,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,1,5,6,8]=>[7,6,5,2,8,4,3,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,1,6,7,4,8]=>[7,6,4,8,3,2,5,1]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,1,7,4,8]=>[7,6,4,3,8,2,5,1]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,6,1,4,7,5,8]=>[7,6,3,8,5,2,4,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,1,4,8]=>[7,6,4,3,2,8,5,1]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,1,4,6,8]=>[7,6,4,2,8,5,3,1]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,1,7,4,5,8]=>[7,6,3,8,2,5,4,1]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,1,4,5,8]=>[7,6,3,2,8,5,4,1]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,1,4,5,6,8]=>[7,6,2,8,5,4,3,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,7,3,8]=>[7,5,8,4,3,2,6,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6,8]=>[7,5,8,4,2,6,3,1]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5,8]=>[7,5,8,3,6,2,4,1]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,4,1,6,7,3,5,8]=>[7,5,8,3,2,6,4,1]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,7,3,5,6,8]=>[7,5,8,2,6,4,3,1]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,7,3,8]=>[7,5,4,8,3,2,6,1]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,4,5,1,7,3,6,8]=>[7,5,4,8,2,6,3,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,1,3,6,7,4,8]=>[7,4,8,6,3,2,5,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,5,1,3,7,4,6,8]=>[7,4,8,6,2,5,3,1]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,1,7,3,8]=>[7,5,4,3,8,2,6,1]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,4,6,1,3,7,5,8]=>[7,5,3,8,6,2,4,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4,8]=>[7,4,8,3,6,2,5,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,5,6,1,3,7,4,8]=>[7,4,3,8,6,2,5,1]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,6,1,3,4,7,5,8]=>[7,3,8,6,5,2,4,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,1,3,8]=>[7,5,4,3,2,8,6,1]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,4,5,7,1,3,6,8]=>[7,5,4,2,8,6,3,1]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,4,6,1,7,3,5,8]=>[7,5,3,8,2,6,4,1]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,1,3,5,8]=>[7,5,3,2,8,6,4,1]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,4,7,1,3,5,6,8]=>[7,5,2,8,6,4,3,1]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,1,6,7,3,4,8]=>[7,4,8,3,2,6,5,1]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,1,7,3,4,6,8]=>[7,4,8,2,6,5,3,1]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,1,7,3,4,8]=>[7,4,3,8,2,6,5,1]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,6,1,3,7,4,5,8]=>[7,3,8,6,2,5,4,1]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,1,3,4,8]=>[7,4,3,2,8,6,5,1]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,1,3,4,6,8]=>[7,4,2,8,6,5,3,1]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,6,1,7,3,4,5,8]=>[7,3,8,2,6,5,4,1]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,1,3,4,5,8]=>[7,3,2,8,6,5,4,1]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,6,8]=>[7,2,8,6,5,4,3,1]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[6,8,5,4,3,2,7,1]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6,8]=>[6,8,5,4,2,7,3,1]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]=>[6,8,5,3,7,2,4,1]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,4,6,7,2,5,8]=>[6,8,5,3,2,7,4,1]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,7,2,5,6,8]=>[6,8,5,2,7,4,3,1]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,2,6,7,4,8]=>[6,8,4,7,3,2,5,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,7,4,6,8]=>[6,8,4,7,2,5,3,1]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,6,2,4,7,5,8]=>[6,8,3,7,5,2,4,1]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]=>[6,8,4,3,2,7,5,1]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[6,8,4,2,7,5,3,1]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,7,4,5,8]=>[6,8,3,7,2,5,4,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[6,8,3,2,7,5,4,1]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,7,2,4,5,6,8]=>[6,8,2,7,5,4,3,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,7,2,8]=>[6,5,8,4,3,2,7,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,5,7,2,6,8]=>[6,5,8,4,2,7,3,1]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5,8]=>[6,5,8,3,7,2,4,1]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,1,6,7,2,5,8]=>[6,5,8,3,2,7,4,1]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,7,2,5,6,8]=>[6,5,8,2,7,4,3,1]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>[5,8,7,4,3,2,6,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>[5,8,7,4,2,6,3,1]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[5,8,7,3,6,2,4,1]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[5,8,7,3,2,6,4,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,7,3,5,6,8]=>[5,8,7,2,6,4,3,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,7,2,8]=>[6,5,4,8,3,2,7,1]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,1,7,2,6,8]=>[6,5,4,8,2,7,3,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,1,2,6,7,4,8]=>[6,4,8,7,3,2,5,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,1,2,7,4,6,8]=>[6,4,8,7,2,5,3,1]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,7,3,6,8]=>[5,8,4,7,2,6,3,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,5,1,2,6,7,3,8]=>[5,4,8,7,3,2,6,1]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,1,2,7,3,6,8]=>[5,4,8,7,2,6,3,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[4,8,7,6,3,2,5,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]=>[4,8,7,6,2,5,3,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,1,7,2,8]=>[6,5,4,3,8,2,7,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,1,2,7,5,8]=>[6,5,3,8,7,2,4,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4,8]=>[6,4,8,3,7,2,5,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,1,2,7,4,8]=>[6,4,3,8,7,2,5,1]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,1,2,4,7,5,8]=>[6,3,8,7,5,2,4,1]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]=>[5,8,4,3,7,2,6,1]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,6,2,3,7,5,8]=>[5,8,3,7,6,2,4,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3,8]=>[5,4,8,3,7,2,6,1]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>[4,8,7,3,6,2,5,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,6,1,2,7,3,8]=>[5,4,3,8,7,2,6,1]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,6,1,2,3,7,5,8]=>[5,3,8,7,6,2,4,1]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,6,2,3,7,4,8]=>[4,8,3,7,6,2,5,1]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,1,2,3,7,4,8]=>[4,3,8,7,6,2,5,1]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[3,8,7,6,5,2,4,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,5,7,1,2,6,8]=>[6,5,4,2,8,7,3,1]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,4,6,1,7,2,5,8]=>[6,5,3,8,2,7,4,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,4,6,7,1,2,5,8]=>[6,5,3,2,8,7,4,1]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,1,2,5,6,8]=>[6,5,2,8,7,4,3,1]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,5,1,6,7,2,4,8]=>[6,4,8,3,2,7,5,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,1,7,2,4,6,8]=>[6,4,8,2,7,5,3,1]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,1,7,2,4,8]=>[6,4,3,8,2,7,5,1]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,1,2,4,8]=>[6,4,3,2,8,7,5,1]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,1,2,4,6,8]=>[6,4,2,8,7,5,3,1]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,6,1,7,2,4,5,8]=>[6,3,8,2,7,5,4,1]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,6,7,1,2,4,5,8]=>[6,3,2,8,7,5,4,1]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,6,8]=>[6,2,8,7,5,4,3,1]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>[5,8,4,3,2,7,6,1]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>[5,8,4,2,7,6,3,1]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,7,3,5,8]=>[5,8,3,7,2,6,4,1]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>[5,8,3,2,7,6,4,1]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,7,2,3,5,6,8]=>[5,8,2,7,6,4,3,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,5,1,6,7,2,3,8]=>[5,4,8,3,2,7,6,1]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,1,7,2,3,6,8]=>[5,4,8,2,7,6,3,1]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>[4,8,7,3,2,6,5,1]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[4,8,7,2,6,5,3,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,6,1,7,2,3,8]=>[5,4,3,8,2,7,6,1]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,6,1,2,7,3,5,8]=>[5,3,8,7,2,6,4,1]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,7,3,4,8]=>[4,8,3,7,2,6,5,1]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,1,2,7,3,4,8]=>[4,3,8,7,2,6,5,1]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5,8]=>[3,8,7,6,2,5,4,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,1,2,3,6,8]=>[5,4,2,8,7,6,3,1]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,1,7,2,3,5,8]=>[5,3,8,2,7,6,4,1]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,1,2,3,5,8]=>[5,3,2,8,7,6,4,1]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,6,8]=>[5,2,8,7,6,4,3,1]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,6,7,2,3,4,8]=>[4,8,3,2,7,6,5,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,1,7,2,3,4,6,8]=>[4,8,2,7,6,5,3,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,1,7,2,3,4,8]=>[4,3,8,2,7,6,5,1]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[3,8,7,2,6,5,4,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,6,8]=>[4,2,8,7,6,5,3,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,7,2,3,4,5,8]=>[3,8,2,7,6,5,4,1]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,1,7]=>[7,6,5,4,3,1,8,2]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,1,8,6]=>[7,6,5,4,2,8,1,3]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,1,6]=>[7,6,5,4,2,1,8,3]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[7,6,5,4,1,8,3,2]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,1,7,8,5]=>[7,6,5,3,8,2,1,4]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,1,8,5,7]=>[7,6,5,3,8,1,4,2]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,1,8,5]=>[7,6,5,3,2,8,1,4]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,1,5,8,6]=>[7,6,5,2,8,4,1,3]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,1,5]=>[7,6,5,3,2,1,8,4]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,1,5,7]=>[7,6,5,3,1,8,4,2]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,1,8,5,6]=>[7,6,5,2,8,1,4,3]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>[7,6,5,2,1,8,4,3]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,1,6,7,8,4]=>[7,6,4,8,3,2,1,5]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,8,6]=>[7,6,4,8,2,5,1,3]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,1,8,4,6,7]=>[7,6,4,8,1,5,3,2]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,1,7,8,4]=>[7,6,4,3,8,2,1,5]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,1,8,4,7]=>[7,6,4,3,8,1,5,2]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,1,4,7,8,5]=>[7,6,3,8,5,2,1,4]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>[7,6,3,8,5,1,4,2]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,1,8,4]=>[7,6,4,3,2,8,1,5]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,1,4,8,6]=>[7,6,4,2,8,5,1,3]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,8,5]=>[7,6,3,8,2,5,1,4]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,1,4,8,5]=>[7,6,3,2,8,5,1,4]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,1,4,5,8,6]=>[7,6,2,8,5,4,1,3]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,1,4]=>[7,6,4,3,2,1,8,5]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[7,6,4,3,1,8,5,2]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,1,8,4,6]=>[7,6,4,2,8,1,5,3]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[7,6,4,2,1,8,5,3]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[7,6,4,1,8,5,3,2]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[7,6,3,8,2,1,5,4]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,1,8,4,5,7]=>[7,6,3,8,1,5,4,2]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,1,8,4,5]=>[7,6,3,2,8,1,5,4]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,1,4,8,5,6]=>[7,6,2,8,5,1,4,3]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>[7,6,3,2,1,8,5,4]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>[7,6,3,1,8,5,4,2]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,7,1,8,4,5,6]=>[7,6,2,8,1,5,4,3]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[7,6,2,1,8,5,4,3]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[7,6,1,8,5,4,3,2]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[7,5,8,4,3,2,1,6]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,1,5,6,8,3,7]=>[7,5,8,4,3,1,6,2]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[7,5,8,4,2,6,1,3]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,1,5,8,3,6,7]=>[7,5,8,4,1,6,3,2]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[7,5,8,3,6,2,1,4]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[7,5,8,3,2,6,1,4]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[7,5,8,2,6,4,1,3]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,1,6,7,8,3,5]=>[7,5,8,3,2,1,6,4]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,1,6,8,3,5,7]=>[7,5,8,3,1,6,4,2]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,8,5,6]=>[7,5,8,2,6,1,4,3]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,1,7,8,3,5,6]=>[7,5,8,2,1,6,4,3]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[7,5,8,1,6,4,3,2]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,1,6,7,8,3]=>[7,5,4,8,3,2,1,6]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[7,5,4,8,3,1,6,2]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,8,6]=>[7,5,4,8,2,6,1,3]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[7,5,4,8,2,1,6,3]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,1,8,3,6,7]=>[7,5,4,8,1,6,3,2]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,1,3,6,7,8,4]=>[7,4,8,6,3,2,1,5]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,1,3,6,8,4,7]=>[7,4,8,6,3,1,5,2]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,1,3,7,4,8,6]=>[7,4,8,6,2,5,1,3]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,1,3,7,8,4,6]=>[7,4,8,6,2,1,5,3]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,1,3,8,4,6,7]=>[7,4,8,6,1,5,3,2]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,1,7,8,3]=>[7,5,4,3,8,2,1,6]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,1,8,3,7]=>[7,5,4,3,8,1,6,2]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,1,3,7,8,5]=>[7,5,3,8,6,2,1,4]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>[7,5,3,8,6,1,4,2]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[7,4,8,3,6,2,1,5]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,8,4,7]=>[7,4,8,3,6,1,5,2]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,1,3,7,8,4]=>[7,4,3,8,6,2,1,5]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,5,6,1,3,8,4,7]=>[7,4,3,8,6,1,5,2]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,1,3,4,7,8,5]=>[7,3,8,6,5,2,1,4]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,1,8,3]=>[7,5,4,3,2,8,1,6]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,1,3,8,6]=>[7,5,4,2,8,6,1,3]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,8,5]=>[7,5,3,8,2,6,1,4]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,1,3,8,5]=>[7,5,3,2,8,6,1,4]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,4,7,1,3,5,8,6]=>[7,5,2,8,6,4,1,3]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[7,4,8,3,2,6,1,5]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[7,4,8,2,6,5,1,3]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,8,4]=>[7,4,3,8,2,6,1,5]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,6,1,3,7,4,8,5]=>[7,3,8,6,2,5,1,4]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,1,3,8,4]=>[7,4,3,2,8,6,1,5]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,1,3,4,8,6]=>[7,4,2,8,6,5,1,3]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[7,3,8,2,6,5,1,4]
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,6,7,1,3,4,8,5]=>[7,3,2,8,6,5,1,4]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,1,3,4,5,8,6]=>[7,2,8,6,5,4,1,3]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,1,3]=>[7,5,4,3,2,1,8,6]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>[7,5,4,3,1,8,6,2]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,7,1,8,3,6]=>[7,5,4,2,8,1,6,3]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>[7,5,4,2,1,8,6,3]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>[7,5,3,8,2,1,6,4]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,1,8,3,5]=>[7,5,3,2,8,1,6,4]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>[7,5,2,8,6,1,4,3]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>[7,5,3,2,1,8,6,4]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,4,7,1,8,3,5,6]=>[7,5,2,8,1,6,4,3]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[7,5,2,1,8,6,4,3]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[7,5,1,8,6,4,3,2]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,1,6,7,8,3,4]=>[7,4,8,3,2,1,6,5]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,5,1,6,8,3,4,7]=>[7,4,8,3,1,6,5,2]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,8,4,6]=>[7,4,8,2,6,1,5,3]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,1,7,8,3,4,6]=>[7,4,8,2,1,6,5,3]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[7,4,3,8,2,1,6,5]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,1,3,7,8,4,5]=>[7,3,8,6,2,1,5,4]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,1,3,8,4,5,7]=>[7,3,8,6,1,5,4,2]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,1,8,3,4]=>[7,4,3,2,8,1,6,5]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>[7,4,2,8,6,1,5,3]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,8,4,5]=>[7,3,8,2,6,1,5,4]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,1,3,8,4,5]=>[7,3,2,8,6,1,5,4]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,1,3,4,8,5,6]=>[7,2,8,6,5,1,4,3]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[7,4,3,2,1,8,6,5]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,5,7,1,8,3,4,6]=>[7,4,2,8,1,6,5,3]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[7,4,2,1,8,6,5,3]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,1,3,4,6,7]=>[7,4,1,8,6,5,3,2]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,1,7,8,3,4,5]=>[7,3,8,2,1,6,5,4]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,1,8,3,4,5]=>[7,3,2,8,1,6,5,4]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,1,3,8,4,5,6]=>[7,2,8,6,1,5,4,3]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[7,3,2,1,8,6,5,4]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,8,1,6,5,4,3]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[7,2,1,8,6,5,4,3]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[7,1,8,6,5,4,3,2]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,2]=>[6,8,5,4,3,2,1,7]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,6,8,2,7]=>[6,8,5,4,3,1,7,2]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,5,7,2,8,6]=>[6,8,5,4,2,7,1,3]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,5,7,8,2,6]=>[6,8,5,4,2,1,7,3]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,5,8,2,6,7]=>[6,8,5,4,1,7,3,2]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,4,6,2,7,8,5]=>[6,8,5,3,7,2,1,4]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,4,6,2,8,5,7]=>[6,8,5,3,7,1,4,2]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,4,6,7,2,8,5]=>[6,8,5,3,2,7,1,4]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,4,6,7,8,2,5]=>[6,8,5,3,2,1,7,4]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,4,6,8,2,5,7]=>[6,8,5,3,1,7,4,2]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,4,7,2,8,5,6]=>[6,8,5,2,7,1,4,3]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,4,7,8,2,5,6]=>[6,8,5,2,1,7,4,3]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[6,8,5,1,7,4,3,2]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,2,6,7,8,4]=>[6,8,4,7,3,2,1,5]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,2,6,8,4,7]=>[6,8,4,7,3,1,5,2]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,2,7,8,4,6]=>[6,8,4,7,2,1,5,3]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,8,4,6,7]=>[6,8,4,7,1,5,3,2]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,7,8,4]=>[6,8,4,3,7,2,1,5]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,5,6,2,8,4,7]=>[6,8,4,3,7,1,5,2]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,6,2,4,7,8,5]=>[6,8,3,7,5,2,1,4]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,6,2,4,8,5,7]=>[6,8,3,7,5,1,4,2]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,5,6,7,2,8,4]=>[6,8,4,3,2,7,1,5]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,8,5]=>[6,8,3,7,2,5,1,4]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,1,6,7,2,4,8,5]=>[6,8,3,2,7,5,1,4]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,7,2,4,5,8,6]=>[6,8,2,7,5,4,1,3]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,8,2,4]=>[6,8,4,3,2,1,7,5]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,5,6,8,2,4,7]=>[6,8,4,3,1,7,5,2]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,5,7,2,8,4,6]=>[6,8,4,2,7,1,5,3]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,5,7,8,2,4,6]=>[6,8,4,2,1,7,5,3]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[6,8,4,1,7,5,3,2]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,2,7,8,4,5]=>[6,8,3,7,2,1,5,4]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,8,4,5,7]=>[6,8,3,7,1,5,4,2]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,7,2,4,8,5,6]=>[6,8,2,7,5,1,4,3]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,6,7,8,2,4,5]=>[6,8,3,2,1,7,5,4]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[6,8,3,1,7,5,4,2]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,8,4,5,6]=>[6,8,2,7,1,5,4,3]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[6,8,2,1,7,5,4,3]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[6,8,1,7,5,4,3,2]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[6,5,8,4,3,2,1,7]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,1,5,6,8,2,7]=>[6,5,8,4,3,1,7,2]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>[6,5,8,4,2,7,1,3]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,1,5,7,8,2,6]=>[6,5,8,4,2,1,7,3]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,5,8,2,6,7]=>[6,5,8,4,1,7,3,2]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[6,5,8,3,7,2,1,4]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,8,5,7]=>[6,5,8,3,7,1,4,2]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[6,5,8,3,2,7,1,4]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,7,2,5,8,6]=>[6,5,8,2,7,4,1,3]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,1,6,7,8,2,5]=>[6,5,8,3,2,1,7,4]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,1,6,8,2,5,7]=>[6,5,8,3,1,7,4,2]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,1,7,8,2,5,6]=>[6,5,8,2,1,7,4,3]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[6,5,8,1,7,4,3,2]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,8,3]=>[5,8,7,4,3,2,1,6]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,2,5,6,8,3,7]=>[5,8,7,4,3,1,6,2]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,5,7,3,8,6]=>[5,8,7,4,2,6,1,3]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,5,7,8,3,6]=>[5,8,7,4,2,1,6,3]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,2,5,8,3,6,7]=>[5,8,7,4,1,6,3,2]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,2,6,3,7,8,5]=>[5,8,7,3,6,2,1,4]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,6,3,8,5,7]=>[5,8,7,3,6,1,4,2]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,2,6,7,3,8,5]=>[5,8,7,3,2,6,1,4]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,2,7,3,5,8,6]=>[5,8,7,2,6,4,1,3]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,2,6,7,8,3,5]=>[5,8,7,3,2,1,6,4]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,2,6,8,3,5,7]=>[5,8,7,3,1,6,4,2]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,2,7,3,8,5,6]=>[5,8,7,2,6,1,4,3]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,2,7,8,3,5,6]=>[5,8,7,2,1,6,4,3]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[5,8,7,1,6,4,3,2]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,6,7,8,2]=>[6,5,4,8,3,2,1,7]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,6,8,2,7]=>[6,5,4,8,3,1,7,2]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,8,6]=>[6,5,4,8,2,7,1,3]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>[6,5,4,8,2,1,7,3]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,8,2,6,7]=>[6,5,4,8,1,7,3,2]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,1,2,6,7,8,4]=>[6,4,8,7,3,2,1,5]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,1,2,6,8,4,7]=>[6,4,8,7,3,1,5,2]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,1,2,7,4,8,6]=>[6,4,8,7,2,5,1,3]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,1,2,7,8,4,6]=>[6,4,8,7,2,1,5,3]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,5,1,2,8,4,6,7]=>[6,4,8,7,1,5,3,2]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,2,6,7,8,3]=>[5,8,4,7,3,2,1,6]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,2,6,8,3,7]=>[5,8,4,7,3,1,6,2]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,8,6]=>[5,8,4,7,2,6,1,3]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,2,7,8,3,6]=>[5,8,4,7,2,1,6,3]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,8,3,6,7]=>[5,8,4,7,1,6,3,2]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,1,2,6,7,8,3]=>[5,4,8,7,3,2,1,6]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,1,2,6,8,3,7]=>[5,4,8,7,3,1,6,2]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,1,2,7,3,8,6]=>[5,4,8,7,2,6,1,3]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,1,2,7,8,3,6]=>[5,4,8,7,2,1,6,3]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,1,2,8,3,6,7]=>[5,4,8,7,1,6,3,2]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,3,6,8,4,7]=>[4,8,7,6,3,1,5,2]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,3,7,4,8,6]=>[4,8,7,6,2,5,1,3]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,3,7,8,4,6]=>[4,8,7,6,2,1,5,3]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,3,8,4,6,7]=>[4,8,7,6,1,5,3,2]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,1,7,8,2]=>[6,5,4,3,8,2,1,7]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,1,8,2,7]=>[6,5,4,3,8,1,7,2]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,1,2,7,8,5]=>[6,5,3,8,7,2,1,4]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,4,6,1,2,8,5,7]=>[6,5,3,8,7,1,4,2]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[6,4,8,3,7,2,1,5]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,8,4,7]=>[6,4,8,3,7,1,5,2]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,1,2,7,8,4]=>[6,4,3,8,7,2,1,5]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[6,4,3,8,7,1,5,2]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,1,2,4,7,8,5]=>[6,3,8,7,5,2,1,4]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,1,2,4,8,5,7]=>[6,3,8,7,5,1,4,2]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,7,8,3]=>[5,8,4,3,7,2,1,6]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,6,2,8,3,7]=>[5,8,4,3,7,1,6,2]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,6,2,3,7,8,5]=>[5,8,3,7,6,2,1,4]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,6,2,3,8,5,7]=>[5,8,3,7,6,1,4,2]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[5,4,8,3,7,2,1,6]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,8,3,7]=>[5,4,8,3,7,1,6,2]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2,6,3,8,4,7]=>[4,8,7,3,6,1,5,2]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,7,8,3]=>[5,4,3,8,7,2,1,6]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[5,4,3,8,7,1,6,2]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,6,1,2,3,7,8,5]=>[5,3,8,7,6,2,1,4]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,1,2,3,8,5,7]=>[5,3,8,7,6,1,4,2]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,6,2,3,7,8,4]=>[4,8,3,7,6,2,1,5]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,6,2,3,8,4,7]=>[4,8,3,7,6,1,5,2]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,6,1,2,3,7,8,4]=>[4,3,8,7,6,2,1,5]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,8,4,7]=>[4,3,8,7,6,1,5,2]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,4,7,8,5]=>[3,8,7,6,5,2,1,4]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,4,8,5,7]=>[3,8,7,6,5,1,4,2]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,1,8,2]=>[6,5,4,3,2,8,1,7]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,1,2,8,6]=>[6,5,4,2,8,7,1,3]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,8,5]=>[6,5,3,8,2,7,1,4]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,1,2,8,5]=>[6,5,3,2,8,7,1,4]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,1,2,5,8,6]=>[6,5,2,8,7,4,1,3]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[6,4,8,3,2,7,1,5]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>[6,4,8,2,7,5,1,3]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,8,4]=>[6,4,3,8,2,7,1,5]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,1,2,7,4,8,5]=>[6,3,8,7,2,5,1,4]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,1,2,8,4]=>[6,4,3,2,8,7,1,5]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,1,2,4,8,6]=>[6,4,2,8,7,5,1,3]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[6,3,8,2,7,5,1,4]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,1,2,4,8,5]=>[6,3,2,8,7,5,1,4]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,1,2,4,5,8,6]=>[6,2,8,7,5,4,1,3]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,7,2,8,3]=>[5,8,4,3,2,7,1,6]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,5,7,2,3,8,6]=>[5,8,4,2,7,6,1,3]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,1,6,7,2,3,8,5]=>[5,8,3,2,7,6,1,4]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,7,2,3,5,8,6]=>[5,8,2,7,6,4,1,3]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[5,4,8,3,2,7,1,6]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>[5,4,8,2,7,6,1,3]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,2,6,7,3,8,4]=>[4,8,7,3,2,6,1,5]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,1,2,7,3,4,8,6]=>[4,8,7,2,6,5,1,3]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,8,3]=>[5,4,3,8,2,7,1,6]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,1,2,7,3,8,5]=>[5,3,8,7,2,6,1,4]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,1,2,7,3,8,4]=>[4,3,8,7,2,6,1,5]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,2,3,7,4,8,5]=>[3,8,7,6,2,5,1,4]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,1,2,8,3]=>[5,4,3,2,8,7,1,6]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,7,1,2,3,8,6]=>[5,4,2,8,7,6,1,3]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,1,7,2,3,8,5]=>[5,3,8,2,7,6,1,4]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,1,2,3,8,5]=>[5,3,2,8,7,6,1,4]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,1,2,3,5,8,6]=>[5,2,8,7,6,4,1,3]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,1,7,2,3,4,8,6]=>[4,8,2,7,6,5,1,3]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[4,3,8,2,7,6,1,5]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,2,7,3,4,8,5]=>[3,8,7,2,6,5,1,4]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,1,2,3,8,4]=>[4,3,2,8,7,6,1,5]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,1,2,3,4,8,6]=>[4,2,8,7,6,5,1,3]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,7,2,3,4,8,5]=>[3,8,2,7,6,5,1,4]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,1,2,3,4,8,5]=>[3,2,8,7,6,5,1,4]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,8,6]=>[2,8,7,6,5,4,1,3]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>[6,5,4,3,1,8,7,2]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,1,8,2,6]=>[6,5,4,2,8,1,7,3]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,1,2,6]=>[6,5,4,2,1,8,7,3]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[6,5,4,1,8,7,3,2]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[6,5,3,8,2,1,7,4]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,4,6,1,8,2,5,7]=>[6,5,3,8,1,7,4,2]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,1,8,2,5]=>[6,5,3,2,8,1,7,4]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,1,2,8,5,6]=>[6,5,2,8,7,1,4,3]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[6,5,3,2,1,8,7,4]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[6,5,3,1,8,7,4,2]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,1,8,2,5,6]=>[6,5,2,8,1,7,4,3]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[6,5,1,8,7,4,3,2]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,1,6,7,8,2,4]=>[6,4,8,3,2,1,7,5]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,1,6,8,2,4,7]=>[6,4,8,3,1,7,5,2]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,1,7,8,2,4,6]=>[6,4,8,2,1,7,5,3]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[6,4,8,1,7,5,3,2]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[6,4,3,8,2,1,7,5]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,4,3,8,1,7,5,2]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,1,2,7,8,4,5]=>[6,3,8,7,2,1,5,4]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,1,2,8,4,5,7]=>[6,3,8,7,1,5,4,2]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,1,8,2,4]=>[6,4,3,2,8,1,7,5]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,1,2,8,4,6]=>[6,4,2,8,7,1,5,3]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,8,4,5]=>[6,3,8,2,7,1,5,4]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[6,3,2,8,7,1,5,4]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,1,2,4,8,5,6]=>[6,2,8,7,5,1,4,3]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[6,4,3,2,1,8,7,5]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[6,4,3,1,8,7,5,2]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,1,8,2,4,6]=>[6,4,2,8,1,7,5,3]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]=>[6,4,1,8,7,5,3,2]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[6,3,8,1,7,5,4,2]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,1,8,2,4,5]=>[6,3,2,8,1,7,5,4]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,1,2,8,4,5,6]=>[6,2,8,7,1,5,4,3]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[6,3,2,1,8,7,5,4]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[6,3,1,8,7,5,4,2]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,1,8,2,4,5,6]=>[6,2,8,1,7,5,4,3]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[6,2,1,8,7,5,4,3]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[6,1,8,7,5,4,3,2]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,8,2,3]=>[5,8,4,3,2,1,7,6]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,5,6,8,2,3,7]=>[5,8,4,3,1,7,6,2]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,5,7,2,8,3,6]=>[5,8,4,2,7,1,6,3]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,5,7,8,2,3,6]=>[5,8,4,2,1,7,6,3]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,5,8,2,3,6,7]=>[5,8,4,1,7,6,3,2]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,2,7,8,3,5]=>[5,8,3,7,2,1,6,4]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,8,3,5,7]=>[5,8,3,7,1,6,4,2]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,6,7,2,8,3,5]=>[5,8,3,2,7,1,6,4]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,7,2,3,8,5,6]=>[5,8,2,7,6,1,4,3]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[5,8,3,1,7,6,4,2]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,8,3,5,6]=>[5,8,2,7,1,6,4,3]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[5,8,2,1,7,6,4,3]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[5,8,1,7,6,4,3,2]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,1,6,7,8,2,3]=>[5,4,8,3,2,1,7,6]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,1,6,8,2,3,7]=>[5,4,8,3,1,7,6,2]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,8,3,6]=>[5,4,8,2,7,1,6,3]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,1,7,8,2,3,6]=>[5,4,8,2,1,7,6,3]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>[5,4,8,1,7,6,3,2]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,2,6,7,8,3,4]=>[4,8,7,3,2,1,6,5]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2,6,8,3,4,7]=>[4,8,7,3,1,6,5,2]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,1,2,7,3,8,4,6]=>[4,8,7,2,6,1,5,3]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,1,2,7,8,3,4,6]=>[4,8,7,2,1,6,5,3]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[4,8,7,1,6,5,3,2]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[5,4,3,8,2,1,7,6]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,1,8,2,3,7]=>[5,4,3,8,1,7,6,2]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,6,1,2,7,8,3,5]=>[5,3,8,7,2,1,6,4]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,1,2,8,3,5,7]=>[5,3,8,7,1,6,4,2]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,2,7,8,3,4]=>[4,8,3,7,2,1,6,5]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,8,3,4,7]=>[4,8,3,7,1,6,5,2]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,1,2,7,8,3,4]=>[4,3,8,7,2,1,6,5]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,8,3,4,7]=>[4,3,8,7,1,6,5,2]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,2,3,7,8,4,5]=>[3,8,7,6,2,1,5,4]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,1,2,3,8,4,5,7]=>[3,8,7,6,1,5,4,2]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,1,8,2,3]=>[5,4,3,2,8,1,7,6]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,8,3,5]=>[5,3,8,2,7,1,6,4]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>[5,3,2,8,7,1,6,4]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,1,2,3,8,5,6]=>[5,2,8,7,6,1,4,3]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,6,7,2,8,3,4]=>[4,8,3,2,7,1,6,5]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,1,7,2,3,8,4,6]=>[4,8,2,7,6,1,5,3]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,2,7,3,8,4,5]=>[3,8,7,2,6,1,5,4]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[4,3,2,8,7,1,6,5]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,1,2,3,8,4,6]=>[4,2,8,7,6,1,5,3]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,7,2,3,8,4,5]=>[3,8,2,7,6,1,5,4]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,1,2,3,8,4,5]=>[3,2,8,7,6,1,5,4]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,8,5,6]=>[2,8,7,6,5,1,4,3]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[5,4,3,1,8,7,6,2]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,1,8,2,3,6]=>[5,4,2,8,1,7,6,3]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[5,4,2,1,8,7,6,3]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[5,4,1,8,7,6,3,2]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,1,7,8,2,3,5]=>[5,3,8,2,1,7,6,4]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[5,3,8,1,7,6,4,2]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,1,2,8,3,5,6]=>[5,2,8,7,1,6,4,3]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[5,3,1,8,7,6,4,2]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[5,2,8,1,7,6,4,3]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]=>[5,2,1,8,7,6,4,3]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[5,1,8,7,6,4,3,2]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,6,7,8,2,3,4]=>[4,8,3,2,1,7,6,5]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,6,8,2,3,4,7]=>[4,8,3,1,7,6,5,2]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,8,3,4,6]=>[4,8,2,7,1,6,5,3]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,1,7,8,2,3,4,6]=>[4,8,2,1,7,6,5,3]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]=>[4,8,1,7,6,5,3,2]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,1,7,8,2,3,4]=>[4,3,8,2,1,7,6,5]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,1,8,2,3,4,7]=>[4,3,8,1,7,6,5,2]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,2,7,8,3,4,5]=>[3,8,7,2,1,6,5,4]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[3,8,7,1,6,5,4,2]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,1,8,2,3,4]=>[4,3,2,8,1,7,6,5]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,1,2,8,3,4,6]=>[4,2,8,7,1,6,5,3]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,8,3,4,5]=>[3,8,2,7,1,6,5,4]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,1,2,8,3,4,5]=>[3,2,8,7,1,6,5,4]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,8,4,5,6]=>[2,8,7,6,1,5,4,3]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[4,3,1,8,7,6,5,2]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,1,8,2,3,4,6]=>[4,2,8,1,7,6,5,3]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[4,2,1,8,7,6,5,3]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[4,1,8,7,6,5,3,2]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[3,8,2,1,7,6,5,4]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[3,8,1,7,6,5,4,2]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[3,2,8,1,7,6,5,4]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[2,8,7,1,6,5,4,3]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[3,1,8,7,6,5,4,2]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[2,8,1,7,6,5,4,3]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
searching the database
Sorry, this map was not found in the database.