Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-3
[.,.]=>[1]=>[1]=>[1,0]
[.,[.,.]]=>[2,1]=>[1,1]=>[1,0,1,0]
[[.,.],.]=>[1,2]=>[2]=>[1,1,0,0]
[.,[.,[.,.]]]=>[3,2,1]=>[1,1,1]=>[1,0,1,0,1,0]
[.,[[.,.],.]]=>[2,3,1]=>[2,1]=>[1,1,0,0,1,0]
[[.,.],[.,.]]=>[3,1,2]=>[1,2]=>[1,0,1,1,0,0]
[[.,[.,.]],.]=>[2,1,3]=>[1,2]=>[1,0,1,1,0,0]
[[[.,.],.],.]=>[1,2,3]=>[3]=>[1,1,1,0,0,0]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]=>[1,0,1,0,1,0,1,0]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]=>[1,1,0,0,1,0,1,0]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]=>[1,1,1,0,0,0,1,0]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2]=>[1,1,0,0,1,1,0,0]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,3]=>[1,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[1,1,2]=>[1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,2]=>[1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3]=>[1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[1,3]=>[1,0,1,1,1,0,0,0]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4]=>[1,1,1,1,0,0,0,0]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]=>[1,1,1,1,0,0,0,0,1,0]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,2,3,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[8,5,6,3,4,7,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,3,8,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[8,6,4,3,5,1,2,7]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[7,5,2,3,4,6,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[6,7,4,3,5,1,2,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[6,7,5,3,2,1,4,8]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[6,7,4,3,1,2,5,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[4,5,3,6,2,1,7,8]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[4,5,6,2,3,1,7,8]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[4,5,3,6,1,2,7,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
bounce path
Description
The bounce path determined by an integer composition.
searching the database
Sorry, this map was not found in the database.