Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]=>1
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]=>0
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>11
[.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>[3,1,2]=>10
[[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>[1,3,2]=>01
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>111
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>[4,3,1,2]=>110
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>[4,1,3,2]=>101
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>[4,2,1,3]=>110
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>[4,1,2,3]=>100
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>[1,4,3,2]=>011
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>[3,4,1,2]=>010
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>[3,1,4,2]=>101
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>[1,2,4,3]=>001
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>110
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>[3,1,2,4]=>100
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>[1,3,2,4]=>010
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[5,4,3,1,2]=>1110
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>[5,4,1,3,2]=>1101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>[5,1,4,3,2]=>1011
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>[5,3,4,1,2]=>1010
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[5,3,1,4,2]=>1101
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[5,1,2,4,3]=>1001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[5,1,3,2,4]=>1010
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>[2,5,4,1,3]=>0110
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>[4,5,1,3,2]=>0101
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>[4,5,2,1,3]=>0110
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>[3,5,1,2,4]=>0100
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>[4,1,5,3,2]=>1011
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>[4,3,5,1,2]=>1010
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>[2,4,5,1,3]=>0010
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>[4,3,1,5,2]=>1101
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>[4,1,2,5,3]=>1001
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>[1,4,2,5,3]=>0101
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>[3,1,2,5,4]=>1001
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[1,2,3,5,4]=>0001
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[4,1,3,2,5]=>1010
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>[3,4,1,2,5]=>0100
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[1,2,4,3,5]=>0010
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>[1,3,2,4,5]=>0100
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>11110
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>11101
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>11110
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>11100
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>[6,5,3,4,1,2]=>11010
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>11101
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>11001
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>11110
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>11100
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>11010
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>11100
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>11000
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>10111
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>[6,2,5,4,1,3]=>10110
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>[6,4,5,1,3,2]=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>[6,4,5,2,1,3]=>10110
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>[6,3,5,1,2,4]=>10100
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>11011
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>[6,4,3,5,1,2]=>11010
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>10011
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>[6,2,4,5,1,3]=>10010
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>11101
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>11001
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>10101
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>11001
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>10001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>11110
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>11100
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>11010
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>11100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>11000
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>10110
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>[6,3,4,1,2,5]=>10100
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>11010
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>10010
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>11100
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>11000
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>10100
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>11000
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>10000
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>[2,6,5,4,1,3]=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>[2,6,5,1,4,3]=>01101
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>[2,6,5,3,1,4]=>01110
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>[5,6,4,1,2,3]=>01100
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>[5,6,1,4,3,2]=>01011
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>[5,6,3,4,1,2]=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>[5,6,3,1,4,2]=>01101
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>[4,6,1,2,5,3]=>01001
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>[5,6,3,2,1,4]=>01110
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>[2,6,4,1,3,5]=>01100
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>[4,6,1,3,2,5]=>01010
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>[4,6,2,1,3,5]=>01100
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>[3,6,1,2,4,5]=>01000
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>10111
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>[5,2,6,4,1,3]=>10110
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>[5,4,6,1,3,2]=>10101
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>[5,4,6,2,1,3]=>10110
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>[4,3,6,1,2,5]=>10100
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>[2,3,6,5,1,4]=>00110
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>[2,5,6,1,4,3]=>00101
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>[2,5,6,3,1,4]=>00110
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>[2,4,6,1,3,5]=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>11011
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>[5,4,3,6,1,2]=>11010
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>10011
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>[5,2,4,6,1,3]=>10010
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>01011
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>[2,5,4,6,1,3]=>01010
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>10011
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>[4,2,5,6,1,3]=>10010
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>00010
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>11101
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>11001
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>10101
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>11001
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>10001
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>01101
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>[4,5,1,2,6,3]=>01001
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>00101
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>11001
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>10001
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>01001
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>00001
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>11100
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>11010
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>11100
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>11000
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>10110
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>[5,3,4,1,2,6]=>10100
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>11010
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>10010
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>11100
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>11000
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>10100
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>11000
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>10000
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>[2,5,4,1,3,6]=>01100
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>[4,5,1,3,2,6]=>01010
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>[4,5,2,1,3,6]=>01100
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>[3,5,1,2,4,6]=>01000
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>10110
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>[4,3,5,1,2,6]=>10100
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>00100
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>11010
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>10010
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>10010
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>00010
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>11000
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>10100
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>11000
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>10000
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>01000
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>111101
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>111110
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>111011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>[7,6,5,3,4,1,2]=>111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>111101
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>111001
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>111110
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>111100
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>111010
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>111100
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>110111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>[7,6,2,5,4,1,3]=>110110
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>[7,6,4,5,1,3,2]=>110101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>[7,6,4,5,2,1,3]=>110110
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>[7,6,3,5,1,2,4]=>110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>111011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>[7,6,4,3,5,1,2]=>111010
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>[7,6,2,4,5,1,3]=>110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>111101
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>111001
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>110101
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>111001
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>110001
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>111110
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>111100
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>111010
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>111100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>111000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>110110
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>[7,6,3,4,1,2,5]=>110100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>111010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>110010
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>111100
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>111000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>110100
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>111000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>101111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>[7,2,6,5,4,1,3]=>101110
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>[7,2,6,5,1,4,3]=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>[7,2,6,5,3,1,4]=>101110
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>[7,5,6,4,1,2,3]=>101100
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>[7,5,6,1,4,3,2]=>101011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>[7,5,6,3,4,1,2]=>101010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>[7,5,6,3,1,4,2]=>101101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>[7,4,6,1,2,5,3]=>101001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>[7,5,6,3,2,1,4]=>101110
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>[7,2,6,4,1,3,5]=>101100
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>[7,4,6,1,3,2,5]=>101010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>[7,4,6,2,1,3,5]=>101100
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>[7,3,6,1,2,4,5]=>101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>110111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>[7,5,2,6,4,1,3]=>110110
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>[7,5,4,6,1,3,2]=>110101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>[7,5,4,6,2,1,3]=>110110
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>[7,4,3,6,1,2,5]=>110100
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>100111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>[7,2,3,6,5,1,4]=>100110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>[7,2,5,6,1,4,3]=>100101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>[7,2,5,6,3,1,4]=>100110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>[7,2,4,6,1,3,5]=>100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>111011
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>[7,5,4,3,6,1,2]=>111010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>110011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>[7,5,2,4,6,1,3]=>110010
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>101011
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>[7,2,5,4,6,1,3]=>101010
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>110011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>[7,4,2,5,6,1,3]=>110010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>100011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>[7,2,3,5,6,1,4]=>100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>111101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>111001
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>110101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>111001
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>110001
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>101101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>[7,4,5,1,2,6,3]=>101001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>110101
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>100101
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>111001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>110001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>101001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>110001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>111110
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>111100
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>111010
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>111100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>111000
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>110110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>[7,5,3,4,1,2,6]=>110100
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>111010
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>110010
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>111100
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>111000
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>110100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>111000
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>110000
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>101110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>[7,2,5,4,1,3,6]=>101100
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>[7,4,5,1,3,2,6]=>101010
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>[7,4,5,2,1,3,6]=>101100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>[7,3,5,1,2,4,6]=>101000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>110110
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>[7,4,3,5,1,2,6]=>110100
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>100110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>[7,2,4,5,1,3,6]=>100100
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>111010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>110010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>101010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>110010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>100010
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>111100
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>111000
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>110100
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>111000
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>110000
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>101100
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>[7,3,4,1,2,5,6]=>101000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>110100
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>100100
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>111000
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>110000
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>101000
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>110000
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>[2,7,6,5,4,1,3]=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>[2,7,6,5,1,4,3]=>011101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>[2,7,6,5,3,1,4]=>011110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>[3,7,6,5,1,2,4]=>011100
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>[2,7,6,1,5,4,3]=>011011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>[3,7,6,4,5,1,2]=>011010
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>[2,7,6,4,1,5,3]=>011101
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>[6,7,5,1,2,4,3]=>011001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>[2,7,6,4,3,1,5]=>011110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>[6,7,5,3,1,2,4]=>011100
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>[6,7,5,1,3,2,4]=>011010
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>[6,7,5,2,1,3,4]=>011100
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>[5,7,6,1,2,3,4]=>011000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>[6,7,1,5,4,3,2]=>010111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>[6,7,2,5,4,1,3]=>010110
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>[6,7,4,5,1,3,2]=>010101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>[6,7,4,5,2,1,3]=>010110
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>[5,7,3,6,1,2,4]=>010100
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>[6,7,4,1,5,3,2]=>011011
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>[6,7,4,3,5,1,2]=>011010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>[5,7,1,2,6,4,3]=>010011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>[5,7,2,4,6,1,3]=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>[6,7,4,3,1,5,2]=>011101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>[2,7,5,1,3,6,4]=>011001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>[5,7,1,4,2,6,3]=>010101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>[5,7,3,1,2,6,4]=>011001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>[4,7,1,2,3,6,5]=>010001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>[6,7,4,3,2,1,5]=>011110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>[2,7,5,4,1,3,6]=>011100
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>[2,7,5,1,4,3,6]=>011010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>[2,7,5,3,1,4,6]=>011100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>[5,7,4,1,2,3,6]=>011000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>[5,7,1,4,3,2,6]=>010110
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>[5,7,3,4,1,2,6]=>010100
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>[5,7,3,1,4,2,6]=>011010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>[4,7,1,2,5,3,6]=>010010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>[5,7,3,2,1,4,6]=>011100
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>[2,7,4,1,3,5,6]=>011000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>[4,7,1,3,2,5,6]=>010100
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>[4,7,2,1,3,5,6]=>011000
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[3,7,1,2,4,5,6]=>010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>101111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>[6,2,7,5,4,1,3]=>101110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>[6,2,7,5,1,4,3]=>101101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>[6,2,7,5,3,1,4]=>101110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>[6,5,7,4,1,2,3]=>101100
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>[6,5,7,1,4,3,2]=>101011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>[6,5,7,3,4,1,2]=>101010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>[6,5,7,3,1,4,2]=>101101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>[5,4,7,1,2,6,3]=>101001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>[6,5,7,3,2,1,4]=>101110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>[5,2,7,4,1,3,6]=>101100
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>[5,4,7,1,3,2,6]=>101010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>[5,4,7,2,1,3,6]=>101100
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>[4,3,7,1,2,5,6]=>101000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>[2,3,7,6,5,1,4]=>001110
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>[2,3,7,6,1,5,4]=>001101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>[2,3,7,6,4,1,5]=>001110
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>[3,6,7,5,1,2,4]=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>[2,6,7,1,5,4,3]=>001011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>[3,6,7,4,5,1,2]=>001010
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>[2,6,7,4,1,5,3]=>001101
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>[2,5,7,1,3,6,4]=>001001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>[2,6,7,4,3,1,5]=>001110
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>[2,3,7,5,1,4,6]=>001100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>[2,5,7,1,4,3,6]=>001010
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>[2,5,7,3,1,4,6]=>001100
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>[2,4,7,1,3,5,6]=>001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>110111
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>[6,5,2,7,4,1,3]=>110110
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>[6,5,4,7,1,3,2]=>110101
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>[6,5,4,7,2,1,3]=>110110
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>[5,4,3,7,1,2,6]=>110100
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>100111
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>[6,2,3,7,5,1,4]=>100110
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>[6,2,5,7,1,4,3]=>100101
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>[6,2,5,7,3,1,4]=>100110
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>[5,2,4,7,1,3,6]=>100100
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>010111
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>[2,6,3,7,5,1,4]=>010110
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>[2,6,5,7,1,4,3]=>010101
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>[2,6,5,7,3,1,4]=>010110
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>[2,5,4,7,1,3,6]=>010100
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>100111
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>[5,2,3,7,6,1,4]=>100110
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>[5,2,6,7,1,4,3]=>100101
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>[5,2,6,7,3,1,4]=>100110
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>[4,2,5,7,1,3,6]=>100100
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>[2,3,4,7,6,1,5]=>000110
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>[2,3,6,7,1,5,4]=>000101
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>[2,3,6,7,4,1,5]=>000110
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,4,6]=>000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>111011
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>[6,5,4,3,7,1,2]=>111010
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>110011
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>[6,5,2,4,7,1,3]=>110010
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>101011
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>[6,2,5,4,7,1,3]=>101010
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>110011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>[6,4,2,5,7,1,3]=>110010
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>100011
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>[6,2,3,5,7,1,4]=>100010
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>011011
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>[2,6,5,4,7,1,3]=>011010
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>[5,6,1,2,7,4,3]=>010011
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>[5,6,2,4,7,1,3]=>010010
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>101011
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>[5,2,6,4,7,1,3]=>101010
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>001011
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>[2,3,6,5,7,1,4]=>001010
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>110011
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>[5,4,2,6,7,1,3]=>110010
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>100011
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>[5,2,3,6,7,1,4]=>100010
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>010011
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>[2,5,3,6,7,1,4]=>010010
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>100011
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>[4,2,3,6,7,1,5]=>100010
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>111101
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>111001
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>110101
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>111001
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>110001
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>101101
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>[6,4,5,1,2,7,3]=>101001
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>110101
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>100101
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>111001
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>110001
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>101001
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>110001
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>100001
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>011101
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>[2,6,5,1,3,7,4]=>011001
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>[5,6,1,4,2,7,3]=>010101
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>[5,6,3,1,2,7,4]=>011001
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>[4,6,1,2,3,7,5]=>010001
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>101101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>[5,4,6,1,2,7,3]=>101001
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>001101
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>[2,5,6,1,3,7,4]=>001001
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>110101
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>100101
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>100101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>111001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>110001
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>101001
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>110001
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>100001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>011001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>[4,5,1,2,3,7,6]=>010001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>101001
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>001001
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>110001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>100001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>010001
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>111100
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>111010
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>111100
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>111000
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>[6,5,3,4,1,2,7]=>110100
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>111010
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>110010
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>111100
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>111000
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>110100
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>111000
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>110000
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>101110
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>[6,2,5,4,1,3,7]=>101100
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>[6,4,5,1,3,2,7]=>101010
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>[6,4,5,2,1,3,7]=>101100
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>[6,3,5,1,2,4,7]=>101000
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>110110
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>[6,4,3,5,1,2,7]=>110100
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>100110
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>[6,2,4,5,1,3,7]=>100100
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>111010
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>110010
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>101010
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>110010
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>100010
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>111100
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>111000
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>110100
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>111000
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>110000
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>101100
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>[6,3,4,1,2,5,7]=>101000
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>110100
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>100100
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>111000
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>110000
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>101000
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>110000
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>100000
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>[2,6,5,4,1,3,7]=>011100
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>[2,6,5,1,4,3,7]=>011010
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>[2,6,5,3,1,4,7]=>011100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>[5,6,4,1,2,3,7]=>011000
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>[5,6,1,4,3,2,7]=>010110
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>[5,6,3,4,1,2,7]=>010100
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>[5,6,3,1,4,2,7]=>011010
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>[4,6,1,2,5,3,7]=>010010
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>[5,6,3,2,1,4,7]=>011100
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>[2,6,4,1,3,5,7]=>011000
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>[4,6,1,3,2,5,7]=>010100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>[4,6,2,1,3,5,7]=>011000
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>[3,6,1,2,4,5,7]=>010000
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>101110
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>[5,2,6,4,1,3,7]=>101100
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>[5,4,6,1,3,2,7]=>101010
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>[5,4,6,2,1,3,7]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>[4,3,6,1,2,5,7]=>101000
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>[2,3,6,5,1,4,7]=>001100
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>[2,5,6,1,4,3,7]=>001010
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>[2,5,6,3,1,4,7]=>001100
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>[2,4,6,1,3,5,7]=>001000
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>110110
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>[5,4,3,6,1,2,7]=>110100
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>100110
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>[5,2,4,6,1,3,7]=>100100
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>010110
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>[2,5,4,6,1,3,7]=>010100
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>100110
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>[4,2,5,6,1,3,7]=>100100
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>000100
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>111010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>110010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>101010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>110010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>100010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>011010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>[4,5,1,2,6,3,7]=>010010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>001010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>110010
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>100010
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>100010
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>000010
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>111000
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>110100
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>111000
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>110000
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>[5,3,4,1,2,6,7]=>101000
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>110100
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>111000
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>110000
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>101000
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>110000
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>[2,5,4,1,3,6,7]=>011000
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>[4,5,1,3,2,6,7]=>010100
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>[4,5,2,1,3,6,7]=>011000
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>[3,5,1,2,4,6,7]=>010000
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>101100
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>[4,3,5,1,2,6,7]=>101000
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>001000
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>010100
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>100100
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>010000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>1111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>1111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[7,5,8,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>1111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>1111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>1111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>1111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>1111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>1111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,6,4,7,5,3,2,1]=>[8,7,6,4,5,1,3,2]=>1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[7,6,4,8,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>1110110
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[6,4,7,8,5,3,2,1]=>[8,7,6,3,5,1,2,4]=>1110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>1111011
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>1110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[7,4,5,8,6,3,2,1]=>[8,7,6,2,4,5,1,3]=>1110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>1111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>1111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>1110101
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>1110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>1111110
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>1111100
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>1111010
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>1111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>1111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>1110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[6,4,7,5,8,3,2,1]=>[8,7,6,3,4,1,2,5]=>1110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>1111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>1110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>1111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>1111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>1110100
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>1111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>1101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[7,8,6,3,5,4,2,1]=>[8,7,2,6,5,4,1,3]=>1101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[8,6,7,3,5,4,2,1]=>[8,7,2,6,5,1,4,3]=>1101101
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,5,3,6,4,2,1]=>[8,7,5,6,1,4,3,2]=>1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[7,5,3,8,6,4,2,1]=>[8,7,5,6,3,4,1,2]=>1101010
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[8,6,5,3,7,4,2,1]=>[8,7,5,6,3,1,4,2]=>1101101
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[7,6,5,3,8,4,2,1]=>[8,7,5,6,3,2,1,4]=>1101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[6,7,3,5,8,4,2,1]=>[8,7,2,6,4,1,3,5]=>1101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,3,6,7,8,4,2,1]=>[8,7,3,6,1,2,4,5]=>1101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>1110111
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[8,6,4,3,7,5,2,1]=>[8,7,5,4,6,1,3,2]=>1110101
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[6,4,3,7,8,5,2,1]=>[8,7,4,3,6,1,2,5]=>1110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>1100111
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[6,3,4,7,8,5,2,1]=>[8,7,2,4,6,1,3,5]=>1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>1111011
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>1110011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>[7,5,3,4,8,6,2,1]=>[8,7,2,5,4,6,1,3]=>1101010
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>1110011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[7,4,3,5,8,6,2,1]=>[8,7,4,2,5,6,1,3]=>1110010
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>1111101
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>1111001
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[3,5,6,4,8,7,2,1]=>[8,5,3,6,4,7,2,1]=>[8,7,4,5,1,2,6,3]=>1101001
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>1110101
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>1110001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>1100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>1111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>1111100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>1111010
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>1110110
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>1111010
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[4,5,7,6,3,8,2,1]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>1110010
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>1111100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>1111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>1110000
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[6,7,3,5,4,8,2,1]=>[8,7,2,5,4,1,3,6]=>1101100
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[7,5,3,6,4,8,2,1]=>[8,7,4,5,1,3,2,6]=>1101010
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[5,3,6,7,4,8,2,1]=>[8,7,3,5,1,2,4,6]=>1101000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>1100110
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[3,4,6,7,5,8,2,1]=>[6,3,4,7,5,8,2,1]=>[8,7,2,4,5,1,3,6]=>1100100
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>1111010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>1101010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>1111100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>1110000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>1101100
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[5,3,6,4,7,8,2,1]=>[8,7,3,4,1,2,5,6]=>1101000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>1100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>1101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>1110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[7,8,6,5,2,4,3,1]=>[8,2,7,6,5,4,1,3]=>1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,6,7,5,2,4,3,1]=>[8,2,7,6,5,1,4,3]=>1011101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[8,6,5,7,2,4,3,1]=>[8,2,7,6,4,1,5,3]=>1011101
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[7,6,5,8,2,4,3,1]=>[8,2,7,6,4,3,1,5]=>1011110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[6,7,5,2,8,4,3,1]=>[8,6,7,5,3,1,2,4]=>1011100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[7,5,6,2,8,4,3,1]=>[8,6,7,5,1,3,2,4]=>1011010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,6,2,7,8,4,3,1]=>[8,5,7,6,1,2,3,4]=>1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,7,6,4,2,5,3,1]=>[8,6,7,1,5,4,3,2]=>1010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,6,4,2,7,5,3,1]=>[8,6,7,4,5,1,3,2]=>1010101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[8,6,5,4,2,7,3,1]=>[8,6,7,4,3,1,5,2]=>1011101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,6,4,2,5,7,3,1]=>[8,5,7,1,4,2,6,3]=>1010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[8,4,2,5,6,7,3,1]=>[8,4,7,1,2,3,6,5]=>1010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[7,6,5,4,2,8,3,1]=>[8,6,7,4,3,2,1,5]=>1011110
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>[6,7,5,2,4,8,3,1]=>[8,2,7,5,4,1,3,6]=>1011100
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>[5,6,2,7,4,8,3,1]=>[8,5,7,4,1,2,3,6]=>1011000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[7,6,4,2,5,8,3,1]=>[8,5,7,1,4,3,2,6]=>1010110
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[7,5,4,2,6,8,3,1]=>[8,5,7,3,1,4,2,6]=>1011010
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[5,6,2,4,7,8,3,1]=>[8,2,7,4,1,3,5,6]=>1011000
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[4,2,5,6,7,8,3,1]=>[8,3,7,1,2,4,5,6]=>1010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>1101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[7,8,6,3,2,5,4,1]=>[8,6,2,7,5,4,1,3]=>1101110
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[3,2,7,6,8,5,4,1]=>[7,6,8,3,2,5,4,1]=>[8,6,2,7,5,3,1,4]=>1101110
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[8,7,5,3,2,6,4,1]=>[8,6,5,7,1,4,3,2]=>1101011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[7,5,3,2,8,6,4,1]=>[8,6,5,7,3,4,1,2]=>1101010
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[7,6,5,3,2,8,4,1]=>[8,6,5,7,3,2,1,4]=>1101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[6,7,3,2,5,8,4,1]=>[8,5,2,7,4,1,3,6]=>1101100
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>1001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[6,7,2,3,8,5,4,1]=>[8,3,6,7,5,1,2,4]=>1001100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,5,2,3,6,7,4,1]=>[8,2,5,7,1,3,6,4]=>1001001
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[2,3,6,5,7,8,4,1]=>[6,5,2,3,7,8,4,1]=>[8,2,5,7,3,1,4,6]=>1001100
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[5,2,3,6,7,8,4,1]=>[8,2,4,7,1,3,5,6]=>1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>1110111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[8,6,4,3,2,7,5,1]=>[8,6,5,4,7,1,3,2]=>1110101
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>1100111
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[6,3,4,2,7,8,5,1]=>[8,5,2,4,7,1,3,6]=>1100100
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,6,4,2,3,7,5,1]=>[8,2,6,5,7,1,4,3]=>1010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>1100111
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>1000111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[7,8,2,3,4,6,5,1]=>[8,2,3,4,7,6,1,5]=>1000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,2,3,4,7,8,5,1]=>[8,2,3,5,7,1,4,6]=>1000100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[7,5,4,3,2,8,6,1]=>[8,6,5,4,3,7,1,2]=>1111010
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[7,4,5,3,2,8,6,1]=>[8,6,5,2,4,7,1,3]=>1110010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>1110011
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>1011011
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[8,7,4,2,5,3,6,1]=>[8,5,6,1,2,7,4,3]=>1010011
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[7,5,2,3,4,8,6,1]=>[8,2,3,6,5,7,1,4]=>1001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>1110011
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[7,2,3,4,5,8,6,1]=>[8,2,3,4,6,7,1,5]=>1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>1111101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[5,6,4,3,2,8,7,1]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>1111001
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>1111001
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>1110101
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>1110001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>1100001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>1101101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>1110101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>1000101
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>1110001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[3,5,4,2,6,8,7,1]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>1101001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>1110001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>1111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>1111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>1111010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>1111100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>1111000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>1110110
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>[6,4,7,5,3,2,8,1]=>[8,6,5,3,4,1,2,7]=>1110100
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>1110010
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>1110100
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>1101110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>1110110
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>1100110
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>1110010
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>1101010
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>1100010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>1110100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>1111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>1110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>1101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[5,3,6,4,7,2,8,1]=>[8,6,3,4,1,2,5,7]=>1101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>1110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>1100100
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>1011110
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[7,5,6,2,4,3,8,1]=>[8,2,6,5,1,4,3,7]=>1011010
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[5,6,2,7,4,3,8,1]=>[8,5,6,4,1,2,3,7]=>1011000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[6,4,2,7,5,3,8,1]=>[8,5,6,3,4,1,2,7]=>1010100
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[7,5,4,2,6,3,8,1]=>[8,5,6,3,1,4,2,7]=>1011010
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[5,6,2,4,7,3,8,1]=>[8,2,6,4,1,3,5,7]=>1011000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[6,4,2,5,7,3,8,1]=>[8,4,6,1,3,2,5,7]=>1010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[5,4,2,6,7,3,8,1]=>[8,4,6,2,1,3,5,7]=>1011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[4,2,5,6,7,3,8,1]=>[8,3,6,1,2,4,5,7]=>1010000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>1001110
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[5,2,3,6,7,4,8,1]=>[8,2,4,6,1,3,5,7]=>1001000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>1010110
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[2,4,3,6,7,5,8,1]=>[6,4,2,3,7,5,8,1]=>[8,2,5,4,6,1,3,7]=>1010100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>1100110
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>1000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>[6,2,3,4,7,5,8,1]=>[8,2,3,5,6,1,4,7]=>1000100
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>1011010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>1101010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>1110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>1010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>1100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>1000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>1111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>1111000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>1110000
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>1100100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>1111000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>1110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>1100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>1011100
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>1001100
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>1000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>1101000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>1110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>1100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>1011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[4,2,5,3,6,7,8,1]=>[8,3,4,1,2,5,6,7]=>1010000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>1001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>1110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>1100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>1010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>1100000
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[7,8,6,5,4,1,3,2]=>[2,8,7,6,5,4,1,3]=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[8,6,7,5,4,1,3,2]=>[2,8,7,6,5,1,4,3]=>0111101
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[6,7,8,5,1,4,3,2]=>[3,8,7,6,5,1,2,4]=>0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[8,7,5,6,4,1,3,2]=>[2,8,7,6,1,5,4,3]=>0111011
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[8,5,6,7,1,4,3,2]=>[3,8,7,6,1,2,5,4]=>0111001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[7,6,5,8,4,1,3,2]=>[2,8,7,6,4,3,1,5]=>0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[6,7,5,8,1,4,3,2]=>[3,8,7,6,4,1,2,5]=>0111100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[7,5,6,8,1,4,3,2]=>[3,8,7,6,1,4,2,5]=>0111010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[6,5,7,8,1,4,3,2]=>[3,8,7,6,2,1,4,5]=>0111100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,6,7,1,8,4,3,2]=>[7,8,6,5,1,2,3,4]=>0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[8,7,6,4,5,1,3,2]=>[2,8,7,1,6,5,4,3]=>0110111
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[8,6,4,7,1,5,3,2]=>[3,8,7,5,6,1,4,2]=>0110101
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[7,6,4,8,1,5,3,2]=>[3,8,7,5,6,2,1,4]=>0110110
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,5,4,8,7,6,3,2]=>[8,7,5,4,6,1,3,2]=>[2,8,7,5,1,6,4,3]=>0111011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[7,5,4,8,1,6,3,2]=>[3,8,7,5,4,6,1,2]=>0111010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[8,5,4,6,1,7,3,2]=>[7,8,6,3,1,2,5,4]=>0111001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[7,6,5,4,8,1,3,2]=>[2,8,7,5,4,3,1,6]=>0111110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[5,4,6,1,7,8,3,2]=>[6,8,7,2,1,3,4,5]=>0111000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[8,7,6,5,3,1,4,2]=>[7,8,1,6,5,4,3,2]=>0101111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[7,8,6,3,1,5,4,2]=>[7,8,2,6,5,4,1,3]=>0101110
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[7,6,8,3,1,5,4,2]=>[7,8,2,6,5,3,1,4]=>0101110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[6,7,3,1,8,5,4,2]=>[7,8,5,6,4,1,2,3]=>0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[8,7,5,3,1,6,4,2]=>[7,8,5,6,1,4,3,2]=>0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[7,5,3,1,8,6,4,2]=>[7,8,5,6,3,4,1,2]=>0101010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[7,6,5,3,1,8,4,2]=>[7,8,5,6,3,2,1,4]=>0101110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[7,5,3,1,6,8,4,2]=>[6,8,4,7,1,3,2,5]=>0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[6,5,3,1,7,8,4,2]=>[6,8,4,7,2,1,3,5]=>0101100
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[5,3,1,6,7,8,4,2]=>[5,8,3,7,1,2,4,6]=>0101000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[8,7,6,4,3,1,5,2]=>[7,8,5,1,6,4,3,2]=>0110111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[7,8,3,1,4,6,5,2]=>[6,8,2,3,7,5,1,4]=>0100110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[8,6,3,1,4,7,5,2]=>[6,8,2,5,7,1,4,3]=>0100101
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[6,3,1,4,7,8,5,2]=>[5,8,2,4,7,1,3,6]=>0100100
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[8,7,5,4,3,1,6,2]=>[7,8,5,4,1,6,3,2]=>0111011
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[7,5,4,3,1,8,6,2]=>[7,8,5,4,3,6,1,2]=>0111010
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[8,7,5,3,1,4,6,2]=>[6,8,1,5,2,7,4,3]=>0101011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[7,5,3,1,4,8,6,2]=>[6,8,2,5,4,7,1,3]=>0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[8,7,4,3,1,5,6,2]=>[6,8,4,1,2,7,5,3]=>0110011
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[8,7,3,1,4,5,6,2]=>[5,8,1,2,3,7,6,4]=>0100011
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[8,6,5,4,3,1,7,2]=>[7,8,5,4,3,1,6,2]=>0111101
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,3,5,6,4,8,7,2]=>[8,5,3,1,6,4,7,2]=>[6,8,4,5,1,2,7,3]=>0101001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[8,6,4,3,1,5,7,2]=>[6,8,4,1,5,2,7,3]=>0110101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,3,4,6,5,8,7,2]=>[8,6,3,1,4,5,7,2]=>[5,8,1,2,6,3,7,4]=>0100101
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,3,5,4,6,8,7,2]=>[8,5,3,1,4,6,7,2]=>[5,8,1,4,2,3,7,6]=>0101001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,4,3,5,6,8,7,2]=>[8,4,3,1,5,6,7,2]=>[5,8,3,1,2,4,7,6]=>0110001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[8,3,1,4,5,6,7,2]=>[4,8,1,2,3,5,7,6]=>0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[7,6,5,4,3,1,8,2]=>[7,8,5,4,3,2,1,6]=>0111110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[6,5,7,4,1,3,8,2]=>[2,8,6,5,3,1,4,7]=>0111100
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[6,4,7,1,5,3,8,2]=>[3,8,6,4,5,1,2,7]=>0110100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[5,4,6,1,7,3,8,2]=>[6,8,5,2,1,3,4,7]=>0111000
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[4,5,1,6,7,3,8,2]=>[5,8,6,1,2,3,4,7]=>0110000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[7,5,3,1,6,4,8,2]=>[6,8,4,5,1,3,2,7]=>0101010
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[5,3,1,6,7,4,8,2]=>[5,8,3,6,1,2,4,7]=>0101000
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[6,4,3,1,7,5,8,2]=>[6,8,4,3,5,1,2,7]=>0110100
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[6,3,1,4,7,5,8,2]=>[5,8,2,4,6,1,3,7]=>0100100
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[7,5,3,1,4,6,8,2]=>[5,8,1,4,2,6,3,7]=>0101010
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[7,4,3,1,5,6,8,2]=>[5,8,3,1,2,6,4,7]=>0110010
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,3,4,5,7,6,8,2]=>[7,3,1,4,5,6,8,2]=>[4,8,1,2,3,6,5,7]=>0100010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[6,5,4,3,1,7,8,2]=>[6,8,4,3,2,1,5,7]=>0111100
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[5,4,6,1,3,7,8,2]=>[2,8,5,3,1,4,6,7]=>0111000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[6,4,3,1,5,7,8,2]=>[5,8,3,1,4,2,6,7]=>0110100
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[6,3,1,4,5,7,8,2]=>[4,8,1,2,5,3,6,7]=>0100100
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[4,5,1,3,6,7,8,2]=>[2,8,4,1,3,5,6,7]=>0110000
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[4,3,1,5,6,7,8,2]=>[4,8,2,1,3,5,6,7]=>0110000
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[3,1,4,5,6,7,8,2]=>[3,8,1,2,4,5,6,7]=>0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[7,8,6,5,2,1,4,3]=>[7,2,8,6,5,4,1,3]=>1011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[8,6,7,5,2,1,4,3]=>[7,2,8,6,5,1,4,3]=>1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[7,6,8,5,2,1,4,3]=>[7,2,8,6,5,3,1,4]=>1011110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[6,7,8,2,1,5,4,3]=>[7,3,8,6,5,1,2,4]=>1011100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[7,5,8,2,1,6,4,3]=>[7,3,8,6,4,5,1,2]=>1011010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[7,6,5,8,2,1,4,3]=>[7,2,8,6,4,3,1,5]=>1011110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[6,7,5,2,1,8,4,3]=>[7,6,8,5,3,1,2,4]=>1011100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[7,5,6,2,1,8,4,3]=>[7,6,8,5,1,3,2,4]=>1011010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[6,5,7,2,1,8,4,3]=>[7,6,8,5,2,1,3,4]=>1011100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>[6,5,8,7,1,2,3,4]=>1011000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[8,7,6,4,2,1,5,3]=>[7,6,8,1,5,4,3,2]=>1010111
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[8,7,5,4,2,1,6,3]=>[7,6,8,4,1,5,3,2]=>1011011
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[8,7,4,2,1,5,6,3]=>[6,5,8,1,2,7,4,3]=>1010011
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[8,6,5,4,2,1,7,3]=>[7,6,8,4,3,1,5,2]=>1011101
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>[8,5,6,2,1,4,7,3]=>[6,2,8,5,1,3,7,4]=>1011001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[8,6,4,2,1,5,7,3]=>[6,5,8,1,4,2,7,3]=>1010101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[8,5,4,2,1,6,7,3]=>[6,5,8,3,1,2,7,4]=>1011001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[8,4,2,1,5,6,7,3]=>[5,4,8,1,2,3,7,6]=>1010001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[7,6,5,4,2,1,8,3]=>[7,6,8,4,3,2,1,5]=>1011110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>[6,7,5,2,1,4,8,3]=>[6,2,8,5,4,1,3,7]=>1011100
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[7,6,4,2,1,5,8,3]=>[6,5,8,1,4,3,2,7]=>1010110
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[6,4,2,1,7,5,8,3]=>[6,5,8,3,4,1,2,7]=>1010100
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[6,5,4,2,1,7,8,3]=>[6,5,8,3,2,1,4,7]=>1011100
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[5,6,2,1,4,7,8,3]=>[5,2,8,4,1,3,6,7]=>1011000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[5,4,2,1,6,7,8,3]=>[5,4,8,2,1,3,6,7]=>1011000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[7,8,6,5,1,2,4,3]=>[2,3,8,7,6,5,1,4]=>0011110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[6,7,8,1,2,5,4,3]=>[3,4,8,7,6,1,2,5]=>0011100
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[8,7,5,6,1,2,4,3]=>[2,3,8,7,1,6,5,4]=>0011011
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[7,5,8,1,2,6,4,3]=>[3,4,8,7,5,6,1,2]=>0011010
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[7,6,5,8,1,2,4,3]=>[2,3,8,7,5,4,1,6]=>0011110
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[7,5,6,1,2,8,4,3]=>[3,7,8,6,1,4,2,5]=>0011010
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[8,7,6,4,1,2,5,3]=>[2,7,8,1,6,5,4,3]=>0010111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[8,6,4,1,2,7,5,3]=>[3,7,8,5,6,1,4,2]=>0010101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[8,7,4,1,2,5,6,3]=>[2,6,8,1,3,7,5,4]=>0010011
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[8,6,5,4,1,2,7,3]=>[2,7,8,5,4,1,6,3]=>0011101
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[8,6,4,1,2,5,7,3]=>[2,6,8,1,5,3,7,4]=>0010101
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[8,4,1,2,5,6,7,3]=>[2,5,8,1,3,4,7,6]=>0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[7,6,5,4,1,2,8,3]=>[2,7,8,5,4,3,1,6]=>0011110
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[5,6,1,2,7,4,8,3]=>[3,6,8,5,1,2,4,7]=>0011000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[7,6,4,1,2,5,8,3]=>[2,6,8,1,5,4,3,7]=>0010110
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[6,4,1,2,7,5,8,3]=>[3,6,8,4,5,1,2,7]=>0010100
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[5,6,1,2,4,7,8,3]=>[2,3,8,5,1,4,6,7]=>0011000
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[5,4,1,2,6,7,8,3]=>[2,5,8,3,1,4,6,7]=>0011000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[4,1,2,5,6,7,8,3]=>[2,4,8,1,3,5,6,7]=>0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>1101111
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[6,7,3,2,1,8,5,4]=>[7,6,5,8,4,1,2,3]=>1101100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[8,7,5,3,2,1,6,4]=>[7,6,5,8,1,4,3,2]=>1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[7,5,3,2,1,8,6,4]=>[7,6,5,8,3,4,1,2]=>1101010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[8,6,5,3,2,1,7,4]=>[7,6,5,8,3,1,4,2]=>1101101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[8,5,3,2,1,6,7,4]=>[6,5,4,8,1,2,7,3]=>1101001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[7,6,5,3,2,1,8,4]=>[7,6,5,8,3,2,1,4]=>1101110
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[5,3,2,1,6,7,8,4]=>[5,4,3,8,1,2,6,7]=>1101000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>1001111
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[8,6,7,2,3,1,5,4]=>[7,2,3,8,6,1,5,4]=>1001101
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,1,5,4]=>[7,2,3,8,6,4,1,5]=>1001110
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[8,7,5,2,3,1,6,4]=>[7,2,6,8,1,5,4,3]=>1001011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[7,5,2,3,1,8,6,4]=>[7,3,6,8,4,5,1,2]=>1001010
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[8,6,5,2,3,1,7,4]=>[7,2,6,8,4,1,5,3]=>1001101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[7,5,2,3,1,6,8,4]=>[6,2,5,8,1,4,3,7]=>1001010
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[6,5,2,3,1,7,8,4]=>[6,2,5,8,3,1,4,7]=>1001100
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[5,2,3,1,6,7,8,4]=>[5,2,4,8,1,3,6,7]=>1001000
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[7,6,8,3,1,2,5,4]=>[2,7,3,8,6,4,1,5]=>0101110
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[8,7,5,3,1,2,6,4]=>[2,7,6,8,1,5,4,3]=>0101011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[7,5,3,1,2,8,6,4]=>[3,7,6,8,4,5,1,2]=>0101010
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,3,2,5,6,8,7,4]=>[8,5,3,1,2,6,7,4]=>[2,6,5,8,1,3,7,4]=>0101001
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[7,6,5,3,1,2,8,4]=>[2,7,6,8,4,3,1,5]=>0101110
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[7,5,3,1,2,6,8,4]=>[2,6,5,8,1,4,3,7]=>0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[6,5,3,1,2,7,8,4]=>[2,6,5,8,3,1,4,7]=>0101100
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,5,4]=>[6,2,3,8,7,5,1,4]=>1001110
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[8,6,7,2,1,3,5,4]=>[6,2,3,8,7,1,5,4]=>1001101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[7,6,8,2,1,3,5,4]=>[6,2,3,8,7,4,1,5]=>1001110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[6,7,2,1,3,8,5,4]=>[6,3,7,8,5,1,2,4]=>1001100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[8,7,5,2,1,3,6,4]=>[6,2,7,8,1,5,4,3]=>1001011
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[5,2,1,3,6,7,8,4]=>[4,2,5,8,1,3,6,7]=>1001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>0001111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[7,6,8,1,2,3,5,4]=>[2,3,4,8,7,5,1,6]=>0001110
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[8,7,5,1,2,3,6,4]=>[2,3,7,8,1,6,5,4]=>0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[7,5,1,2,3,8,6,4]=>[3,4,7,8,5,6,1,2]=>0001010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[8,6,5,1,2,3,7,4]=>[2,3,7,8,5,1,6,4]=>0001101
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[8,5,1,2,3,6,7,4]=>[2,3,6,8,1,4,7,5]=>0001001
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[6,7,1,2,3,5,8,4]=>[2,3,4,8,6,1,5,7]=>0001100
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[6,5,1,2,3,7,8,4]=>[2,3,6,8,4,1,5,7]=>0001100
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[5,1,2,3,6,7,8,4]=>[2,3,5,8,1,4,6,7]=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[7,8,4,3,2,1,6,5]=>[7,6,5,2,8,4,1,3]=>1110110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[8,6,4,3,2,1,7,5]=>[7,6,5,4,8,1,3,2]=>1110101
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[7,6,4,3,2,1,8,5]=>[7,6,5,4,8,2,1,3]=>1110110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[6,4,3,2,1,7,8,5]=>[6,5,4,3,8,1,2,7]=>1110100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>1100111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[7,8,3,4,2,1,6,5]=>[7,6,2,3,8,5,1,4]=>1100110
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[7,6,3,4,2,1,8,5]=>[7,6,2,5,8,3,1,4]=>1100110
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[6,3,4,2,1,7,8,5]=>[6,5,2,4,8,1,3,7]=>1100100
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>1010111
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>1100111
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[7,8,3,2,4,1,6,5]=>[7,5,2,3,8,6,1,4]=>1100110
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[8,6,3,2,4,1,7,5]=>[7,5,2,6,8,1,4,3]=>1100101
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>1000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[7,8,2,3,4,1,6,5]=>[7,2,3,4,8,6,1,5]=>1000110
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[8,6,2,3,4,1,7,5]=>[7,2,3,6,8,1,5,4]=>1000101
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[7,6,2,3,4,1,8,5]=>[7,2,3,6,8,4,1,5]=>1000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[6,2,3,4,1,7,8,5]=>[6,2,3,5,8,1,4,7]=>1000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>0110111
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,4,3,2,7,8,6,5]=>[7,8,4,3,1,2,6,5]=>[2,7,6,3,8,5,1,4]=>0110110
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[7,6,4,3,1,2,8,5]=>[2,7,6,5,8,3,1,4]=>0110110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[6,4,3,1,2,7,8,5]=>[2,6,5,4,8,1,3,7]=>0110100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[8,7,6,3,1,4,2,5]=>[6,7,1,2,8,5,4,3]=>0100111
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[8,6,3,1,4,2,7,5]=>[6,7,2,5,8,1,4,3]=>0100101
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[7,8,4,2,1,3,6,5]=>[6,2,7,3,8,5,1,4]=>1010110
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[8,6,4,2,1,3,7,5]=>[6,2,7,5,8,1,4,3]=>1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[7,6,4,2,1,3,8,5]=>[6,2,7,5,8,3,1,4]=>1010110
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>0010111
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[8,6,4,1,2,3,7,5]=>[2,3,7,6,8,1,5,4]=>0010101
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[6,4,1,2,3,7,8,5]=>[2,3,6,5,8,1,4,7]=>0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[7,8,3,2,1,4,6,5]=>[6,5,2,3,8,7,1,4]=>1100110
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[8,6,3,2,1,4,7,5]=>[6,5,2,7,8,1,4,3]=>1100101
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[6,3,2,1,4,7,8,5]=>[5,4,2,6,8,1,3,7]=>1100100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>1000111
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,3,2,4,7,8,6,5]=>[7,8,3,1,2,4,6,5]=>[2,6,3,4,8,7,1,5]=>0100110
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[8,6,3,1,2,4,7,5]=>[2,6,3,7,8,1,5,4]=>0100101
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[7,8,2,1,3,4,6,5]=>[5,2,3,4,8,7,1,6]=>1000110
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[6,2,1,3,4,7,8,5]=>[4,2,3,6,8,1,5,7]=>1000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[7,8,1,2,3,4,6,5]=>[2,3,4,5,8,7,1,6]=>0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[8,6,1,2,3,4,7,5]=>[2,3,4,7,8,1,6,5]=>0000101
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[6,1,2,3,4,7,8,5]=>[2,3,4,6,8,1,5,7]=>0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[7,5,4,3,2,1,8,6]=>[7,6,5,4,3,8,1,2]=>1111010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>1110011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>1100011
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[8,7,4,2,5,3,1,6]=>[7,5,6,1,2,8,4,3]=>1010011
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>1101011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[7,4,3,2,5,1,8,6]=>[7,5,4,2,6,8,1,3]=>1110010
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>1100011
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[7,4,2,3,5,1,8,6]=>[7,2,5,3,6,8,1,4]=>1010010
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>1000011
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[7,2,3,4,5,1,8,6]=>[7,2,3,4,6,8,1,5]=>1000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>0111011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[8,7,4,5,1,3,2,6]=>[2,7,6,1,3,8,5,4]=>0110011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,3,5,4,2,8,7,6]=>[8,7,5,3,1,4,2,6]=>[6,7,1,5,2,8,4,3]=>0101011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[7,5,3,1,4,2,8,6]=>[6,7,2,5,4,8,1,3]=>0101010
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[8,7,3,1,4,5,2,6]=>[5,7,1,2,3,8,6,4]=>0100011
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[7,3,1,4,5,2,8,6]=>[5,7,2,3,6,8,1,4]=>0100010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[7,5,4,1,2,3,8,6]=>[2,3,7,6,5,8,1,4]=>0011010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[8,7,4,1,2,5,3,6]=>[2,6,7,1,3,8,5,4]=>0010011
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>1101011
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[2,3,1,5,4,7,8,6]=>[7,5,2,3,1,4,8,6]=>[6,2,3,7,5,8,1,4]=>1001010
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[7,5,3,1,2,4,8,6]=>[2,6,3,7,5,8,1,4]=>0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[7,5,1,2,3,4,8,6]=>[2,3,4,7,6,8,1,5]=>0001010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[7,4,3,2,1,5,8,6]=>[6,5,4,2,7,8,1,3]=>1110010
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[3,4,2,1,5,7,8,6]=>[7,3,4,2,1,5,8,6]=>[6,5,2,3,7,8,1,4]=>1100010
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>1100011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>1000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[7,2,3,4,1,5,8,6]=>[6,2,3,4,7,8,1,5]=>1000010
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[8,7,3,1,4,2,5,6]=>[5,6,1,2,3,8,7,4]=>0100011
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[7,3,1,4,2,5,8,6]=>[5,6,2,3,7,8,1,4]=>0100010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>0010011
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>1100011
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>1000011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>1000011
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,1,2,3,4,5,8,6]=>[2,3,4,5,7,8,1,6]=>0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>1111001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>1110101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>1111001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>1110001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>1101101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[8,5,3,6,4,2,1,7]=>[7,6,4,5,1,2,8,3]=>1101001
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>1110101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>1110001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>1110001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>1100001
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[2,5,4,6,3,1,8,7]=>[8,5,4,2,6,3,1,7]=>[7,5,6,3,1,2,8,4]=>1011001
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[8,5,3,2,6,4,1,7]=>[7,5,4,6,1,2,8,3]=>1101001
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>1001101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>1110101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>1010101
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[3,2,4,6,5,1,8,7]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>1100101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>1110001
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>1101001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>1100001
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>0111101
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>[8,5,6,4,1,3,2,7]=>[2,7,6,5,1,3,8,4]=>0111001
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,3,5,6,4,2,8,7]=>[8,5,3,1,6,4,2,7]=>[6,7,4,5,1,2,8,3]=>0101001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[8,5,6,2,1,4,3,7]=>[6,2,7,5,1,3,8,4]=>1011001
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>0011101
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,2,5,4,6,3,8,7]=>[8,5,4,1,2,6,3,7]=>[2,6,7,4,1,3,8,5]=>0011001
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[8,4,1,2,5,6,3,7]=>[2,5,7,1,3,4,8,6]=>0010001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>1101101
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[8,5,3,2,1,6,4,7]=>[6,5,4,7,1,2,8,3]=>1101001
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>1001101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>0001101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>1100101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>1100101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>1000101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>0110101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[8,6,3,1,4,2,5,7]=>[5,6,1,2,7,3,8,4]=>0100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>0010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>1100101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>1111001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>1100001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[8,4,2,5,3,1,6,7]=>[6,4,5,1,2,3,8,7]=>1010001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>1010001
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>1000001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[8,4,5,1,3,2,6,7]=>[2,6,5,1,3,4,8,7]=>0110001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>1011001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[8,4,2,1,5,3,6,7]=>[5,4,6,1,2,3,8,7]=>1010001
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[8,4,1,2,5,3,6,7]=>[2,5,6,1,3,4,8,7]=>0010001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>1101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>0001001
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>1000001
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>1111100
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>1111010
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>1111100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>1111000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>1110110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[6,4,7,5,3,2,1,8]=>[7,6,5,3,4,1,2,8]=>1110100
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>1111010
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>1110010
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>1111000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>1110000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>1111010
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>1110010
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>1111100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>1111000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>1111000
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>1111000
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>1100000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[2,6,5,7,4,3,1,8]=>[6,5,7,2,4,3,1,8]=>[7,2,6,5,3,1,4,8]=>1011100
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[5,6,2,7,4,3,1,8]=>[7,5,6,4,1,2,3,8]=>1011000
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[7,6,4,2,5,3,1,8]=>[7,5,6,1,4,3,2,8]=>1010110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[6,4,2,7,5,3,1,8]=>[7,5,6,3,4,1,2,8]=>1010100
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[7,4,2,5,6,3,1,8]=>[7,4,6,1,2,5,3,8]=>1010010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>1101110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[3,2,6,5,7,4,1,8]=>[6,5,3,2,7,4,1,8]=>[7,5,4,6,2,1,3,8]=>1101100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[5,3,2,6,7,4,1,8]=>[7,4,3,6,1,2,5,8]=>1101000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>1110110
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[2,4,3,7,6,5,1,8]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>1010110
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[3,2,4,7,6,5,1,8]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>1100110
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[6,3,2,4,7,5,1,8]=>[7,4,2,5,6,1,3,8]=>1100100
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>1110010
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[2,5,4,3,7,6,1,8]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>1011010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>1101010
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>1111100
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>1111000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[5,3,6,4,2,7,1,8]=>[7,5,3,4,1,2,6,8]=>1101000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>1100100
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>1111000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>1110000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>1101000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[5,4,2,6,3,7,1,8]=>[7,4,5,2,1,3,6,8]=>1011000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>1101100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>1010100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>1100100
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>1000100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>1111000
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>1100000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>1011000
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>1001000
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>1110000
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>1100000
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[2,4,3,5,6,7,1,8]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>1010000
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>1100000
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>[6,7,5,4,1,3,2,8]=>[2,7,6,5,4,1,3,8]=>0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,5,7,6,4,3,2,8]=>[7,5,6,4,1,3,2,8]=>[2,7,6,5,1,4,3,8]=>0111010
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[6,5,7,4,1,3,2,8]=>[2,7,6,5,3,1,4,8]=>0111100
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,4,6,7,5,3,2,8]=>[6,4,7,1,5,3,2,8]=>[3,7,6,4,5,1,2,8]=>0110100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[7,5,3,1,6,4,2,8]=>[6,7,4,5,1,3,2,8]=>0101010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[7,5,3,1,4,6,2,8]=>[5,7,1,4,2,6,3,8]=>0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[7,4,3,1,5,6,2,8]=>[5,7,3,1,2,6,4,8]=>0110010
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[4,5,1,6,3,7,2,8]=>[5,7,4,1,2,3,6,8]=>0110000
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[6,5,3,1,4,7,2,8]=>[5,7,1,4,3,2,6,8]=>0101100
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[5,3,1,6,4,7,2,8]=>[5,7,3,4,1,2,6,8]=>0101000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[6,4,3,1,5,7,2,8]=>[5,7,3,1,4,2,6,8]=>0110100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[5,4,3,1,6,7,2,8]=>[5,7,3,2,1,4,6,8]=>0111000
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[3,1,4,5,6,7,2,8]=>[3,7,1,2,4,5,6,8]=>0100000
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[7,6,4,2,1,5,3,8]=>[6,5,7,1,4,3,2,8]=>1010110
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[2,1,4,6,5,7,3,8]=>[6,4,2,1,5,7,3,8]=>[5,4,7,1,3,2,6,8]=>1010100
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,2,4,5,7,6,3,8]=>[7,4,1,2,5,6,3,8]=>[2,5,7,1,3,6,4,8]=>0010010
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[6,4,1,2,5,7,3,8]=>[2,5,7,1,4,3,6,8]=>0010100
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[5,4,1,2,6,7,3,8]=>[2,5,7,3,1,4,6,8]=>0011000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>1101110
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[5,3,2,1,6,7,4,8]=>[5,4,3,7,1,2,6,8]=>1101000
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8]=>[7,6,5,2,3,1,4,8]=>[6,1,2,7,5,4,3,8]=>1001110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[6,7,2,3,1,5,4,8]=>[6,2,3,7,5,1,4,8]=>1001100
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[7,5,3,1,2,6,4,8]=>[2,6,5,7,1,4,3,8]=>0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[6,5,3,1,2,7,4,8]=>[2,6,5,7,3,1,4,8]=>0101100
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[5,1,2,3,6,7,4,8]=>[2,3,5,7,1,4,6,8]=>0001000
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[6,4,3,2,1,7,5,8]=>[6,5,4,3,7,1,2,8]=>1110100
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>1000110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[6,4,3,1,2,7,5,8]=>[2,6,5,4,7,1,3,8]=>0110100
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>1010110
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>1100110
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[6,3,2,1,4,7,5,8]=>[5,4,2,6,7,1,3,8]=>1100100
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[6,1,2,3,4,7,5,8]=>[2,3,4,6,7,1,5,8]=>0000100
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>1110010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>1011010
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[7,4,2,5,3,1,6,8]=>[6,4,5,1,2,7,3,8]=>1010010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>1101010
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>1000010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[7,5,3,1,4,2,6,8]=>[5,6,1,4,2,7,3,8]=>0101010
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[7,3,1,4,5,2,6,8]=>[4,6,1,2,3,7,5,8]=>0100010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>1001010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>1110010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>0110010
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>1111000
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>1111000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>1110000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>1101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>1111000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[5,4,2,6,3,1,7,8]=>[6,4,5,2,1,3,7,8]=>1011000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>1110100
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>1111000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>1110000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>1110000
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>1100000
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>1001000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>1110000
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[3,2,4,5,6,1,7,8]=>[6,2,1,3,4,5,7,8]=>1100000
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[6,5,3,1,4,2,7,8]=>[5,6,1,4,3,2,7,8]=>0101100
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[5,3,1,6,4,2,7,8]=>[5,6,3,4,1,2,7,8]=>0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>[5,6,3,1,4,2,7,8]=>0110100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[5,4,3,1,6,2,7,8]=>[5,6,3,2,1,4,7,8]=>0111000
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[3,1,4,5,6,2,7,8]=>[3,6,1,2,4,5,7,8]=>0100000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[5,6,2,1,4,3,7,8]=>[5,2,6,4,1,3,7,8]=>1011000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>[5,4,6,1,3,2,7,8]=>1010100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[6,4,1,2,5,3,7,8]=>[2,5,6,1,4,3,7,8]=>0010100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[4,1,2,5,6,3,7,8]=>[2,4,6,1,3,5,7,8]=>0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[5,3,2,1,6,4,7,8]=>[5,4,3,6,1,2,7,8]=>1101000
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[5,1,2,3,6,4,7,8]=>[2,3,5,6,1,4,7,8]=>0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>1110100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>0110100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>1100100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>1010000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[4,5,1,3,2,6,7,8]=>[2,5,4,1,3,6,7,8]=>0110000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[5,3,1,4,2,6,7,8]=>[4,5,1,3,2,6,7,8]=>0101000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>[3,5,1,2,4,6,7,8]=>0100000
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[4,2,1,5,3,6,7,8]=>[4,3,5,1,2,6,7,8]=>1010000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>0010000
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>0101000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>11111101
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>111111100
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[6,8,9,7,5,4,3,2,1]=>[8,6,9,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,1,2]=>11111010
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>111111000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>111110000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>111100000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>[4,2,5,6,7,8,9,3,1]=>[9,3,8,1,2,4,5,6,7]=>10100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,2,4,5,6,7,8]=>01000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>11111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>11111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>11111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>11111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>11111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>11111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>111111110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,3,5,7,9,10,8,6,4,2]=>[9,7,5,3,1,10,8,6,4,2]=>[9,10,7,8,5,6,3,4,1,2]=>010101010
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>111100000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>10100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>11000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>110000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[8,1,2,3,4,5,6,9,7]=>[2,3,4,5,6,8,9,1,7]=>00000010
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[7,1,2,3,4,5,8,9,6]=>[2,3,4,5,7,9,1,6,8]=>00000100
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[9,1,2,3,4,5,6,7,10,8]=>[2,3,4,5,6,7,9,10,1,8]=>000000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[8,9,7,6,5,4,1,3,2]=>[2,9,8,7,6,5,4,1,3]=>01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>11111100
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[9,10,8,7,6,5,4,1,3,2]=>[2,10,9,8,7,6,5,4,1,3]=>011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>111110000
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>10011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>11001111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>10111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>11000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>11111101
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>11111000
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>11111100
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>111111100
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[8,6,5,4,3,2,1,9,7]=>[8,7,6,5,4,3,9,1,2]=>11111010
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>[4,2,1,5,3,6,7,8,9]=>[4,3,5,1,2,6,7,8,9]=>10100000
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>11111100
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>11000000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>11111100
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>11100000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>01000000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>111111100
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>11110000
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>111100000
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,6,5,4,3,1,2,8,9,10,11]=>1111100000
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>111110000
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[5,6,4,3,2,7,1,8,9]=>[7,5,4,3,1,2,6,8,9]=>11110000
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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