Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,[.,.]]=>[2,1]=>[1,2]=>0=>[2]
[[.,.],.]=>[1,2]=>[2,1]=>1=>[1,1]
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>00=>[3]
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>01=>[2,1]
[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>10=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>01=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>11=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>000=>[4]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>001=>[3,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>010=>[2,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>001=>[3,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>011=>[2,1,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>100=>[1,3]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101=>[1,2,1]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>010=>[2,2]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>110=>[1,1,2]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>001=>[3,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>011=>[2,1,1]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>101=>[1,2,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>011=>[2,1,1]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>111=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0000=>[5]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>0001=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>0010=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>0001=>[4,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>0011=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>0100=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>0101=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>0010=>[3,2]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110=>[2,1,2]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>0001=>[4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>0011=>[3,1,1]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>0101=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>0011=>[3,1,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>0111=>[2,1,1,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1001=>[1,3,1]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011=>[1,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100=>[2,3]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101=>[2,2,1]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101=>[1,1,2,1]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0010=>[3,2]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>0110=>[2,1,2]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010=>[1,2,2]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0110=>[2,1,2]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110=>[1,1,1,2]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>0001=>[4,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>0011=>[3,1,1]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>0101=>[2,2,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>0011=>[3,1,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>0111=>[2,1,1,1]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>1001=>[1,3,1]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>1011=>[1,2,1,1]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>0101=>[2,2,1]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>1101=>[1,1,2,1]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>0011=>[3,1,1]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>0111=>[2,1,1,1]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>1011=>[1,2,1,1]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>0111=>[2,1,1,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>1111=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>00001=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>00010=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>00001=>[5,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>00011=>[4,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00010=>[4,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110=>[3,1,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>00001=>[5,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>00011=>[4,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>00101=>[3,2,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>00011=>[4,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>00111=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01001=>[2,3,1]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011=>[2,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100=>[3,3]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101=>[3,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100=>[2,1,3]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101=>[2,1,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>00010=>[4,2]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>00110=>[3,1,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010=>[2,2,2]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>00110=>[3,1,2]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110=>[2,1,1,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>00001=>[5,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>00011=>[4,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>00101=>[3,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>00011=>[4,1,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>00111=>[3,1,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01001=>[2,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01011=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>00101=>[3,2,1]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01101=>[2,1,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>00011=>[4,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>00111=>[3,1,1,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>01011=>[2,2,1,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>00111=>[3,1,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>01111=>[2,1,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001=>[1,4,1]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011=>[1,3,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010=>[1,3,2]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110=>[1,2,1,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001=>[1,4,1]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011=>[1,3,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101=>[1,2,2,1]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011=>[1,3,1,1]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111=>[1,2,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000=>[2,4]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001=>[2,3,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010=>[2,2,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001=>[2,3,1]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011=>[2,2,1,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000=>[1,1,4]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001=>[1,1,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010=>[1,1,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001=>[1,1,3,1]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011=>[1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100=>[3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101=>[3,2,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100=>[2,1,3]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101=>[2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100=>[1,2,3]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101=>[1,2,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100=>[2,1,3]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101=>[2,1,2,1]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100=>[1,1,1,3]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101=>[1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010=>[4,2]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110=>[3,1,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010=>[2,2,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110=>[3,1,2]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110=>[2,1,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010=>[1,3,2]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110=>[1,2,1,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010=>[1,1,2,2]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110=>[3,1,2]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110=>[2,1,1,2]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110=>[1,2,1,2]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110=>[2,1,1,2]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110=>[1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>00001=>[5,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>00011=>[4,1,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>00101=>[3,2,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>00011=>[4,1,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>00111=>[3,1,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>01001=>[2,3,1]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>01011=>[2,2,1,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>00101=>[3,2,1]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>01101=>[2,1,2,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>00011=>[4,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>00111=>[3,1,1,1]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>01011=>[2,2,1,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>00111=>[3,1,1,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>01111=>[2,1,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>10001=>[1,4,1]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>10011=>[1,3,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101=>[1,2,2,1]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>10011=>[1,3,1,1]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>10111=>[1,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001=>[2,3,1]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011=>[2,2,1,1]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001=>[1,1,3,1]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011=>[1,1,2,1,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00101=>[3,2,1]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>01101=>[2,1,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101=>[1,2,2,1]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>01101=>[2,1,2,1]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11101=>[1,1,1,2,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>00011=>[4,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>00111=>[3,1,1,1]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>01011=>[2,2,1,1]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>00111=>[3,1,1,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>01111=>[2,1,1,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>10011=>[1,3,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>10111=>[1,2,1,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>01011=>[2,2,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11011=>[1,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>00111=>[3,1,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>01111=>[2,1,1,1,1]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>10111=>[1,2,1,1,1]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>01111=>[2,1,1,1,1]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111=>[1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>000001=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>000010=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>000001=>[6,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>000011=>[5,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000010=>[5,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110=>[4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>000001=>[6,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>000011=>[5,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>000101=>[4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>000011=>[5,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001001=>[3,3,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100=>[4,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101=>[4,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100=>[3,1,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101=>[3,1,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>000010=>[5,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>000110=>[4,1,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010=>[3,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>000110=>[4,1,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110=>[3,1,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>000001=>[6,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>000011=>[5,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>000101=>[4,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>000011=>[5,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>000111=>[4,1,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001001=>[3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001011=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>000101=>[4,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001101=>[3,1,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>000011=>[5,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>000111=>[4,1,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>001011=>[3,2,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>000111=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>001111=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001=>[2,4,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011=>[2,3,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010=>[2,3,2]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110=>[2,2,1,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001=>[2,4,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011=>[2,3,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101=>[2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011=>[2,3,1,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111=>[2,2,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000=>[3,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001=>[3,3,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010=>[3,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001=>[3,3,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011=>[3,2,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000=>[2,1,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010=>[2,1,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001=>[2,1,3,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011=>[2,1,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100=>[4,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101=>[4,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100=>[3,1,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101=>[3,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100=>[2,2,3]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101=>[2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100=>[3,1,3]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101=>[3,1,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100=>[2,1,1,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101=>[2,1,1,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010=>[5,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110=>[4,1,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010=>[3,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110=>[4,1,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110=>[3,1,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010=>[2,3,2]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110=>[2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010=>[3,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010=>[2,1,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110=>[4,1,2]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110=>[3,1,1,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110=>[2,2,1,2]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110=>[3,1,1,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110=>[2,1,1,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>000001=>[6,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>000011=>[5,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>000101=>[4,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>000011=>[5,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>000111=>[4,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>001001=>[3,3,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>001011=>[3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>000101=>[4,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>001101=>[3,1,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>000011=>[5,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>000111=>[4,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>001011=>[3,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>000111=>[4,1,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>001111=>[3,1,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>010001=>[2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>010011=>[2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101=>[2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>010011=>[2,3,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>010111=>[2,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001=>[3,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011=>[3,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001=>[2,1,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011=>[2,1,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>000101=>[4,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>001101=>[3,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>001101=>[3,1,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011101=>[2,1,1,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>000011=>[5,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>000111=>[4,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>001011=>[3,2,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>000111=>[4,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>001111=>[3,1,1,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>010011=>[2,3,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>010111=>[2,2,1,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>001011=>[3,2,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011011=>[2,1,2,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>000111=>[4,1,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>001111=>[3,1,1,1,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>010111=>[2,2,1,1,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>001111=>[3,1,1,1,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>011111=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001=>[1,5,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011=>[1,4,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010=>[1,4,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001=>[1,5,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011=>[1,4,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101=>[1,3,2,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011=>[1,4,1,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111=>[1,3,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001=>[1,2,3,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011=>[1,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100=>[1,3,3]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101=>[1,3,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100=>[1,2,1,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101=>[1,2,1,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010=>[1,4,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110=>[1,3,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010=>[1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110=>[1,3,1,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110=>[1,2,1,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001=>[1,5,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011=>[1,4,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101=>[1,3,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011=>[1,4,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111=>[1,3,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001=>[1,2,3,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011=>[1,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101=>[1,3,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101=>[1,2,1,2,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011=>[1,4,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111=>[1,3,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011=>[1,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111=>[1,3,1,1,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000=>[2,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001=>[2,4,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010=>[2,3,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001=>[2,4,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011=>[2,3,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100=>[2,2,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101=>[2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010=>[2,3,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110=>[2,2,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001=>[2,4,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011=>[2,3,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101=>[2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011=>[2,3,1,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111=>[2,2,1,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000=>[1,1,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001=>[1,1,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010=>[1,1,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001=>[1,1,4,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011=>[1,1,3,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101=>[1,1,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010=>[1,1,3,2]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110=>[1,1,2,1,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001=>[1,1,4,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011=>[1,1,3,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101=>[1,1,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011=>[1,1,3,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000=>[3,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001=>[3,3,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010=>[3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001=>[3,3,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011=>[3,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000=>[2,1,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001=>[2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010=>[2,1,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001=>[2,1,3,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011=>[2,1,2,1,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000=>[1,2,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001=>[1,2,3,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010=>[1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001=>[1,2,3,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011=>[1,2,2,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000=>[2,1,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001=>[2,1,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010=>[2,1,2,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001=>[2,1,3,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011=>[2,1,2,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001=>[1,1,1,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010=>[1,1,1,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001=>[1,1,1,3,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100=>[4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101=>[4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100=>[3,1,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101=>[3,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100=>[2,2,3]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101=>[2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100=>[3,1,3]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101=>[3,1,2,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100=>[2,1,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101=>[2,1,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100=>[1,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101=>[1,3,2,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100=>[1,2,1,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101=>[1,2,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100=>[2,2,3]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101=>[2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100=>[1,1,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101=>[1,1,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100=>[3,1,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101=>[3,1,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100=>[2,1,1,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101=>[2,1,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100=>[1,2,1,3]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101=>[1,2,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100=>[2,1,1,3]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101=>[2,1,1,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100=>[1,1,1,1,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101=>[1,1,1,1,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010=>[5,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110=>[4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010=>[3,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110=>[4,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110=>[3,1,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010=>[2,3,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110=>[2,2,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010=>[3,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010=>[2,1,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110=>[4,1,2]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110=>[3,1,1,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110=>[2,2,1,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110=>[3,1,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110=>[2,1,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010=>[1,4,2]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110=>[1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010=>[1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110=>[1,3,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110=>[1,2,1,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010=>[2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110=>[2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010=>[1,1,3,2]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110=>[1,1,2,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010=>[3,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010=>[2,1,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010=>[1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010=>[2,1,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010=>[1,1,1,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110=>[4,1,2]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110=>[3,1,1,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110=>[2,2,1,2]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110=>[3,1,1,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110=>[2,1,1,1,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110=>[1,3,1,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110=>[1,2,1,1,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110=>[2,2,1,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110=>[1,1,2,1,2]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110=>[3,1,1,2]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110=>[2,1,1,1,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110=>[1,2,1,1,2]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110=>[2,1,1,1,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>000001=>[6,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>000011=>[5,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>000101=>[4,2,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>000011=>[5,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>000111=>[4,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>001001=>[3,3,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>001011=>[3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>000101=>[4,2,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>001101=>[3,1,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>000011=>[5,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>000111=>[4,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>001011=>[3,2,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>000111=>[4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>001111=>[3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>010001=>[2,4,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>010011=>[2,3,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101=>[2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>010011=>[2,3,1,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>010111=>[2,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001=>[3,3,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011=>[3,2,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001=>[2,1,3,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011=>[2,1,2,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>000101=>[4,2,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>001101=>[3,1,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101=>[2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>001101=>[3,1,2,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>011101=>[2,1,1,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>000011=>[5,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>000111=>[4,1,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>001011=>[3,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>000111=>[4,1,1,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>001111=>[3,1,1,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>010011=>[2,3,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>010111=>[2,2,1,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>001011=>[3,2,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>011011=>[2,1,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>000111=>[4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>001111=>[3,1,1,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>010111=>[2,2,1,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>001111=>[3,1,1,1,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>011111=>[2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001=>[1,5,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011=>[1,4,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101=>[1,3,2,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011=>[1,4,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111=>[1,3,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001=>[1,2,3,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011=>[1,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101=>[1,3,2,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101=>[1,2,1,2,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011=>[1,4,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111=>[1,3,1,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011=>[1,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111=>[1,3,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111=>[1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001=>[2,4,1]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011=>[2,3,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101=>[2,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011=>[2,3,1,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111=>[2,2,1,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001=>[1,1,4,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011=>[1,1,3,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101=>[1,1,2,2,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011=>[1,1,3,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111=>[1,1,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001=>[3,3,1]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011=>[3,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001=>[2,1,3,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011=>[2,1,2,1,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001=>[1,2,3,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011=>[1,2,2,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001=>[2,1,3,1]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011=>[2,1,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001=>[1,1,1,3,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011=>[1,1,1,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101=>[4,2,1]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101=>[3,1,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101=>[2,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101=>[3,1,2,1]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101=>[2,1,1,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101=>[1,3,2,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101=>[1,2,1,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101=>[2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101=>[1,1,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101=>[3,1,2,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101=>[2,1,1,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101=>[1,2,1,2,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101=>[2,1,1,2,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101=>[1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>000011=>[5,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>000111=>[4,1,1,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>001011=>[3,2,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>000111=>[4,1,1,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>001111=>[3,1,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>010011=>[2,3,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>010111=>[2,2,1,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>001011=>[3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>011011=>[2,1,2,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>000111=>[4,1,1,1]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>001111=>[3,1,1,1,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>010111=>[2,2,1,1,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>001111=>[3,1,1,1,1]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>011111=>[2,1,1,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>100011=>[1,4,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>100111=>[1,3,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011=>[1,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>100111=>[1,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>101111=>[1,2,1,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011=>[2,3,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111=>[2,2,1,1,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011=>[1,1,3,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111=>[1,1,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>001011=>[3,2,1,1]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>011011=>[2,1,2,1,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011=>[1,2,2,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>011011=>[2,1,2,1,1]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111011=>[1,1,1,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>000111=>[4,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>001111=>[3,1,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>010111=>[2,2,1,1,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>001111=>[3,1,1,1,1]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>011111=>[2,1,1,1,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>100111=>[1,3,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>101111=>[1,2,1,1,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>010111=>[2,2,1,1,1]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>110111=>[1,1,2,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>001111=>[3,1,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>011111=>[2,1,1,1,1,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>101111=>[1,2,1,1,1,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>011111=>[2,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000=>[8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>0000001=>[7,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>0000010=>[6,2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>0000001=>[7,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>0000011=>[6,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100=>[5,3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>0000101=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000010=>[6,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>0000110=>[5,1,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>0000001=>[7,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>0000011=>[6,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>0000101=>[5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>0000011=>[6,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000=>[4,4]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>0001001=>[4,3,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>0001011=>[4,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100=>[5,3]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0000101=>[5,2,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>0001101=>[4,1,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0000010=>[6,2]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>0000110=>[5,1,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>0001010=>[4,2,2]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>0000110=>[5,1,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>0001110=>[4,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>0000001=>[7,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>0000011=>[6,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>0000101=>[5,2,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>0000011=>[6,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>0000111=>[5,1,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001001=>[4,3,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>0001011=>[4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>0000101=>[5,2,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>0001101=>[4,1,2,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>0000011=>[6,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>0000111=>[5,1,1,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>0001011=>[4,2,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>0000111=>[5,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000=>[3,5]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001=>[3,4,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010001=>[3,4,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100=>[3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101=>[3,2,2,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>0010001=>[3,4,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>0010011=>[3,3,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010101=>[3,2,2,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>0010111=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>0001001=>[4,3,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>0001011=>[4,2,1,1]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>0011001=>[3,1,3,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>0011001=>[3,1,3,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100=>[5,3]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0000101=>[5,2,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>0001100=>[4,1,3]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>0011100=>[3,1,1,3]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0000010=>[6,2]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>0010110=>[3,2,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>0000001=>[7,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>0000011=>[6,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>0001001=>[4,3,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>0001011=>[4,2,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>0000101=>[5,2,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>0000011=>[6,1,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>0001011=>[4,2,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>0000111=>[5,1,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0010001=>[3,4,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>0010011=>[3,3,1,1]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>0010011=>[3,3,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>0010111=>[3,2,1,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>0001001=>[4,3,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011001=>[3,1,3,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>0010101=>[3,2,2,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>0000011=>[6,1,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>0001011=>[4,2,1,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>0010111=>[3,2,1,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011011=>[3,1,2,1,1]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>0001111=>[4,1,1,1,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>0010111=>[3,2,1,1,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000=>[2,6]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010=>[2,4,2]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100001=>[2,5,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101=>[2,3,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>0100110=>[2,3,1,2]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100001=>[2,5,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>0100011=>[2,4,1,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100101=>[2,3,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>0100111=>[2,3,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000=>[2,2,4]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010=>[2,2,2,2]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>0101001=>[2,2,3,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>0101011=>[2,2,2,1,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010=>[2,4,2]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>0100110=>[2,3,1,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>0101010=>[2,2,2,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>0100001=>[2,5,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>0100101=>[2,3,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>0100011=>[2,4,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>0101001=>[2,2,3,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>0101101=>[2,2,1,2,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>0100011=>[2,4,1,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>0100111=>[2,3,1,1,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000=>[3,5]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001=>[3,4,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010=>[3,3,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0010001=>[3,4,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>0010011=>[3,3,1,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100=>[3,2,3]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101=>[3,2,2,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010=>[3,3,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>0010001=>[3,4,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>0010011=>[3,3,1,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0010101=>[3,2,2,1]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>0010011=>[3,3,1,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>0010111=>[3,2,1,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>0110000=>[2,1,5]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>0110010=>[2,1,3,2]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>0110001=>[2,1,4,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>0110011=>[2,1,3,1,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110=>[2,1,2,1,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>0110001=>[2,1,4,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110101=>[2,1,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000=>[4,4]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001=>[4,3,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010=>[4,2,2]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0001001=>[4,3,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>0001011=>[4,2,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>0011000=>[3,1,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>0011001=>[3,1,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0011010=>[3,1,2,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>0011001=>[3,1,3,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>0011011=>[3,1,2,1,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0101000=>[2,2,4]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>0101001=>[2,2,3,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0101010=>[2,2,2,2]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>0101001=>[2,2,3,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0101011=>[2,2,2,1,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>0011000=>[3,1,4]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>0011001=>[3,1,3,1]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>0011001=>[3,1,3,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>0011011=>[3,1,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100=>[5,3]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0000101=>[5,2,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0100100=>[2,3,3]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0010100=>[3,2,3]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>0010101=>[3,2,2,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0110100=>[2,1,2,3]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>0001101=>[4,1,2,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>0101100=>[2,2,1,3]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010=>[6,2]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>0010110=>[3,2,1,2]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>0001010=>[4,2,2]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>0011010=>[3,1,2,2]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>0001110=>[4,1,1,2]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010=>[2,4,2]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>0100110=>[2,3,1,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>0101010=>[2,2,2,2]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>0110010=>[2,1,3,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>0101010=>[2,2,2,2]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>0000110=>[5,1,2]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>0010110=>[3,2,1,2]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>0100110=>[2,3,1,2]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>0010110=>[3,2,1,2]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>0000001=>[7,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>0000111=>[5,1,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>0001001=>[4,3,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>0000101=>[5,2,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>0001101=>[4,1,2,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>0001011=>[4,2,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0010001=>[3,4,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>0010101=>[3,2,2,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>0010011=>[3,3,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>0001001=>[4,3,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>0000101=>[5,2,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>0001101=>[4,1,2,1]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[1,8,2,6,5,3,4,7]=>0001101=>[4,1,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>0000011=>[6,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>0001011=>[4,2,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>0000111=>[5,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>0010011=>[3,3,1,1]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>0011011=>[3,1,2,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>0000111=>[5,1,1,1]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>0001111=>[4,1,1,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>0010111=>[3,2,1,1,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0100001=>[2,5,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0101001=>[2,2,3,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0101011=>[2,2,2,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>0100101=>[2,3,2,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>0100111=>[2,3,1,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>0010001=>[3,4,1]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0010011=>[3,3,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>0010011=>[3,3,1,1]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>0010111=>[3,2,1,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0110001=>[2,1,4,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>0110111=>[2,1,2,1,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001=>[2,2,3,1]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0101011=>[2,2,2,1,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>0011011=>[3,1,2,1,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111011=>[2,1,1,2,1,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>0000101=>[5,2,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0100101=>[2,3,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>0010101=>[3,2,2,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>0000011=>[6,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>0000111=>[5,1,1,1]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>0001111=>[4,1,1,1,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>0001011=>[4,2,1,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>0000111=>[5,1,1,1]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>0001111=>[4,1,1,1,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>0100011=>[2,4,1,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>0100111=>[2,3,1,1,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>0101011=>[2,2,2,1,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>0100111=>[2,3,1,1,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>0010011=>[3,3,1,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0110011=>[2,1,3,1,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>0001011=>[4,2,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>0101011=>[2,2,2,1,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111011=>[2,1,1,2,1,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>0000111=>[5,1,1,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>0010111=>[3,2,1,1,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>0011111=>[3,1,1,1,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>0100111=>[2,3,1,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>0101111=>[2,2,1,1,1,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>0010111=>[3,2,1,1,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>0110111=>[2,1,2,1,1,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>0001111=>[4,1,1,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>0011111=>[3,1,1,1,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000=>[1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001=>[1,6,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100=>[1,4,3]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101=>[1,4,2,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001=>[1,6,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>1000011=>[1,5,1,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101=>[1,4,2,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>1000011=>[1,5,1,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001=>[1,3,3,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>1001011=>[1,3,2,1,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>1001101=>[1,3,1,2,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1000001=>[1,6,1]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>1000011=>[1,5,1,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>1000011=>[1,5,1,1]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011=>[1,3,2,1,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>1000011=>[1,5,1,1]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>1001011=>[1,3,2,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>1000111=>[1,4,1,1,1]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>1001111=>[1,3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000=>[1,2,5]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001=>[1,2,4,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100=>[1,2,2,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101=>[1,2,2,2,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001=>[1,2,4,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011=>[1,2,3,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010011=>[1,2,3,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001=>[1,3,3,1]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001=>[1,2,1,3,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101=>[1,4,2,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101=>[1,3,1,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101=>[1,2,2,2,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101=>[1,3,1,2,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101=>[1,2,1,1,2,1]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>1000110=>[1,4,1,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>1000001=>[1,6,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>1001011=>[1,3,2,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1000101=>[1,4,2,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>1000011=>[1,5,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>1001011=>[1,3,2,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>1000111=>[1,4,1,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>1001111=>[1,3,1,1,1,1]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1010011=>[1,2,3,1,1]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>1010011=>[1,2,3,1,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>1011001=>[1,2,1,3,1]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>1011011=>[1,2,1,2,1,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101=>[1,2,2,2,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>1000011=>[1,5,1,1]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>1000111=>[1,4,1,1,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>1001011=>[1,3,2,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>1010011=>[1,2,3,1,1]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1010111=>[1,2,2,1,1,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>1001011=>[1,3,2,1,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011011=>[1,2,1,2,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>1000111=>[1,4,1,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>1001111=>[1,3,1,1,1,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>1010111=>[1,2,2,1,1,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>1001111=>[1,3,1,1,1,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>1011111=>[1,2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000=>[2,6]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001=>[2,5,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010=>[2,4,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001=>[2,5,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>0100011=>[2,4,1,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101=>[2,3,2,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>0100011=>[2,4,1,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0100111=>[2,3,1,1,1]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001=>[2,2,3,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010=>[2,2,2,2]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101=>[2,3,2,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010=>[2,2,2,2]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110=>[2,3,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>0100001=>[2,5,1]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>0100011=>[2,4,1,1]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>0100011=>[2,4,1,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101=>[2,3,2,1]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>0101101=>[2,2,1,2,1]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>0100011=>[2,4,1,1]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>0100111=>[2,3,1,1,1]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>0101011=>[2,2,2,1,1]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>0100111=>[2,3,1,1,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000=>[1,1,6]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100001=>[1,1,5,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110=>[1,1,3,1,2]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100001=>[1,1,5,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101=>[1,1,3,2,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111=>[1,1,3,1,1,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010=>[1,1,2,2,2]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100=>[1,1,3,3]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010=>[1,1,4,2]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1100001=>[1,1,5,1]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>1100111=>[1,1,3,1,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101001=>[1,1,2,3,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101011=>[1,1,2,2,1,1]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1100101=>[1,1,3,2,1]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101=>[1,1,2,1,2,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>1100011=>[1,1,4,1,1]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>1100111=>[1,1,3,1,1,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1100111=>[1,1,3,1,1,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>1101111=>[1,1,2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000=>[3,5]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001=>[3,4,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010=>[3,3,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001=>[3,4,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011=>[3,3,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100=>[3,2,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101=>[3,2,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010=>[3,3,2]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110=>[3,2,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001=>[3,4,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011=>[3,3,1,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101=>[3,2,2,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>0010011=>[3,3,1,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111=>[3,2,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000=>[2,1,5]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101=>[2,1,2,2,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>0110001=>[2,1,4,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>0110011=>[2,1,3,1,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101=>[2,1,2,2,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000=>[1,2,5]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001=>[1,2,4,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010=>[1,2,3,2]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001=>[1,2,4,1]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011=>[1,2,3,1,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100=>[1,2,2,3]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101=>[1,2,2,2,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010=>[1,2,3,2]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110=>[1,2,2,1,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001=>[1,2,4,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1010011=>[1,2,3,1,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101=>[1,2,2,2,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1010011=>[1,2,3,1,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000=>[2,1,5]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010=>[2,1,3,2]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>0110011=>[2,1,3,1,1]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100=>[2,1,2,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101=>[2,1,2,2,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>0110001=>[2,1,4,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>0110011=>[2,1,3,1,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101=>[2,1,2,2,1]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>0110011=>[2,1,3,1,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000=>[1,1,1,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110001=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010=>[1,1,1,3,2]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110001=>[1,1,1,4,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110011=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110011=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000=>[4,4]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>0001011=>[4,2,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000=>[3,1,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>0011011=>[3,1,2,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000=>[2,2,4]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0101001=>[2,2,3,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010=>[2,2,2,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001=>[2,2,3,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011=>[2,2,2,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000=>[3,1,4]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>0011001=>[3,1,3,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011=>[3,1,2,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000=>[2,1,1,4]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>0111011=>[2,1,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000=>[1,3,4]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011=>[1,3,2,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000=>[1,2,1,4]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001=>[1,2,1,3,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011=>[1,2,1,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000=>[2,2,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010=>[2,2,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011=>[2,2,2,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000=>[1,1,2,4]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001=>[1,1,2,3,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011=>[1,1,2,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000=>[3,1,4]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0011001=>[3,1,3,1]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011=>[3,1,2,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>0111000=>[2,1,1,4]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>0111011=>[2,1,1,2,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000=>[1,2,1,4]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011=>[1,2,1,2,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000=>[2,1,1,4]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010=>[2,1,1,2,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011=>[2,1,1,2,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000=>[1,1,1,1,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111001=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101=>[5,2,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>0101101=>[2,2,1,2,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>0010101=>[3,2,2,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>0001101=>[4,1,2,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>0011101=>[3,1,1,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>0011101=>[3,1,1,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>0111101=>[2,1,1,1,2,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1011100=>[1,2,1,1,3]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101=>[2,3,2,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100=>[1,1,2,1,3]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100=>[1,2,2,3]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101=>[1,2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100=>[2,1,2,3]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101=>[2,1,2,2,1]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100=>[1,1,1,2,3]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101=>[1,1,1,2,2,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0001101=>[4,1,2,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>0011101=>[3,1,1,2,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101=>[1,2,1,1,2,1]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101=>[2,2,1,2,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101=>[1,1,2,1,2,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101=>[3,1,1,2,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>0111101=>[2,1,1,1,2,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101=>[1,2,1,1,2,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100=>[2,1,1,1,3]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>0111101=>[2,1,1,1,2,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101=>[1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010=>[6,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>0001110=>[4,1,1,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>0000110=>[5,1,2]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>0001110=>[4,1,1,2]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>0010110=>[3,2,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>0001110=>[4,1,1,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>0011110=>[3,1,1,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>0101010=>[2,2,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0110010=>[2,1,3,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010=>[2,2,2,2]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>0011010=>[3,1,2,2]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>0000110=>[5,1,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>0001110=>[4,1,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>0010110=>[3,2,1,2]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>0101110=>[2,2,1,1,2]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110=>[1,2,2,1,2]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010=>[1,2,1,2,2]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1001110=>[1,3,1,1,2]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>1001110=>[1,3,1,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010=>[2,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110=>[2,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010=>[2,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>0100110=>[2,3,1,2]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110=>[1,1,3,1,2]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110=>[1,1,3,1,2]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010=>[2,1,3,2]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0110110=>[2,1,2,1,2]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010=>[2,1,3,2]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110=>[2,1,2,1,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010=>[1,1,1,3,2]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110=>[1,1,1,2,1,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010=>[4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>0011010=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>0101010=>[2,2,2,2]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>0011010=>[3,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010=>[1,1,2,2,2]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>0111010=>[2,1,1,2,2]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>0001110=>[4,1,1,2]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>0011110=>[3,1,1,1,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>0010110=>[3,2,1,2]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>0110110=>[2,1,2,1,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110=>[1,1,3,1,2]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110=>[1,2,2,1,2]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110=>[1,1,1,2,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0001110=>[4,1,1,2]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>0011110=>[3,1,1,1,2]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>0101110=>[2,2,1,1,2]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>0011110=>[3,1,1,1,2]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>0111110=>[2,1,1,1,1,2]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110=>[1,3,1,1,2]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>1011110=>[1,2,1,1,1,2]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110=>[3,1,1,1,2]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>0111110=>[2,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>0000001=>[7,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>0000111=>[5,1,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>0001001=>[4,3,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>0001011=>[4,2,1,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>0001101=>[4,1,2,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>0000011=>[6,1,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>0001011=>[4,2,1,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>0001111=>[4,1,1,1,1]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>0010011=>[3,3,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>0010101=>[3,2,2,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>0010111=>[3,2,1,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>0001001=>[4,3,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>0011001=>[3,1,3,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>0001101=>[4,1,2,1]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>0011101=>[3,1,1,2,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>0000011=>[6,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>0000111=>[5,1,1,1]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>0001111=>[4,1,1,1,1]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>0011011=>[3,1,2,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>0000111=>[5,1,1,1]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>0001111=>[4,1,1,1,1]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>0100101=>[2,3,2,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>0100111=>[2,3,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001=>[2,2,3,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0101011=>[2,2,2,1,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>0101101=>[2,2,1,2,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>0100111=>[2,3,1,1,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>0101011=>[2,2,2,1,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[8,1,3,2,7,6,4,5]=>0100111=>[2,3,1,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>0010001=>[3,4,1]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>0010011=>[3,3,1,1]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>0010111=>[3,2,1,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0110001=>[2,1,4,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>0110011=>[2,1,3,1,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>0110101=>[2,1,2,2,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>0110011=>[2,1,3,1,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>0110111=>[2,1,2,1,1,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>0101001=>[2,2,3,1]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>0101011=>[2,2,2,1,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>0011001=>[3,1,3,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>0111001=>[2,1,1,3,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>0000101=>[5,2,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>0010101=>[3,2,2,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>0001101=>[4,1,2,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0101101=>[2,2,1,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>0010101=>[3,2,2,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>0000111=>[5,1,1,1]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>0001111=>[4,1,1,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>0010111=>[3,2,1,1,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>0001011=>[4,2,1,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>0011011=>[3,1,2,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>0000111=>[5,1,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>0001111=>[4,1,1,1,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>0010111=>[3,2,1,1,1]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>0101111=>[2,2,1,1,1,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>0010011=>[3,3,1,1]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>0010111=>[3,2,1,1,1]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>0110111=>[2,1,2,1,1,1]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>0011011=>[3,1,2,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>0101011=>[2,2,2,1,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>0011011=>[3,1,2,1,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>0000111=>[5,1,1,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>0010111=>[3,2,1,1,1]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>0100111=>[2,3,1,1,1]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>0110111=>[2,1,2,1,1,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>0001111=>[4,1,1,1,1]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>0101111=>[2,2,1,1,1,1]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1001101=>[1,3,1,2,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101=>[1,2,2,2,1]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101=>[1,2,2,2,1]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[8,2,1,6,5,3,4,7]=>1001101=>[1,3,1,2,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>1000011=>[1,5,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>1001011=>[1,3,2,1,1]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1011011=>[1,2,1,2,1,1]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>1000111=>[1,4,1,1,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1011111=>[1,2,1,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001=>[2,5,1]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>0100011=>[2,4,1,1]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>0100101=>[2,3,2,1]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>0101001=>[2,2,3,1]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011=>[2,2,2,1,1]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>0100101=>[2,3,2,1]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>0101101=>[2,2,1,2,1]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>0100011=>[2,4,1,1]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001=>[1,1,5,1]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>1100011=>[1,1,4,1,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>1100101=>[1,1,3,2,1]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>1100111=>[1,1,3,1,1,1]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001=>[1,1,2,3,1]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011=>[1,1,2,2,1,1]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101=>[1,1,3,2,1]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>1101101=>[1,1,2,1,2,1]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>1100011=>[1,1,4,1,1]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>1100111=>[1,1,3,1,1,1]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>1100111=>[1,1,3,1,1,1]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>1101111=>[1,1,2,1,1,1,1]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>0110001=>[2,1,4,1]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>0110011=>[2,1,3,1,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>0110101=>[2,1,2,2,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001=>[1,2,4,1]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>1010011=>[1,2,3,1,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101=>[1,2,2,2,1]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1010111=>[1,2,2,1,1,1]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>0110101=>[2,1,2,2,1]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>0110111=>[2,1,2,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001=>[1,1,1,4,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1110011=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101=>[1,1,1,2,2,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>1110011=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1110111=>[1,1,1,2,1,1,1]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>0011001=>[3,1,3,1]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[8,5,1,2,4,3,7,6]=>0011011=>[3,1,2,1,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>0101001=>[2,2,3,1]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>0101011=>[2,2,2,1,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>0011001=>[3,1,3,1]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>0011011=>[3,1,2,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011=>[1,2,1,2,1,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001=>[2,2,3,1]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001=>[1,1,2,3,1]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011=>[1,1,2,2,1,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>0011011=>[3,1,2,1,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001=>[1,2,1,3,1]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111011=>[1,1,1,1,2,1,1]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>0001101=>[4,1,2,1]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>0010101=>[3,2,2,1]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>0001101=>[4,1,2,1]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>0011101=>[3,1,1,2,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>0010101=>[3,2,2,1]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>0110101=>[2,1,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>0001101=>[4,1,2,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>0011101=>[3,1,1,2,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>0101101=>[2,2,1,2,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>0111101=>[2,1,1,1,2,1]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101=>[1,2,2,2,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>1001101=>[1,3,1,2,1]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1011101=>[1,2,1,1,2,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101=>[1,1,3,2,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>0110101=>[2,1,2,2,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101=>[1,2,2,2,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101=>[1,1,1,2,2,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0001101=>[4,1,2,1]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>0011101=>[3,1,1,2,1]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>0101101=>[2,2,1,2,1]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>0111101=>[2,1,1,1,2,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101=>[1,3,1,2,1]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>0111101=>[2,1,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101=>[1,2,1,1,2,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101=>[1,1,1,1,1,2,1]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>0000111=>[5,1,1,1]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>0000111=>[5,1,1,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>0010011=>[3,3,1,1]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>0010111=>[3,2,1,1,1]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>0011011=>[3,1,2,1,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>0000111=>[5,1,1,1]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>0001111=>[4,1,1,1,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>0100111=>[2,3,1,1,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>0101011=>[2,2,2,1,1]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>0100111=>[2,3,1,1,1]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>0011011=>[3,1,2,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>0000111=>[5,1,1,1]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>0001111=>[4,1,1,1,1]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>0010111=>[3,2,1,1,1]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>0110111=>[2,1,2,1,1,1]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>0001111=>[4,1,1,1,1]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011=>[1,5,1,1]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>1000111=>[1,4,1,1,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>1001011=>[1,3,2,1,1]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>1000111=>[1,4,1,1,1]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>1001111=>[1,3,1,1,1,1]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1010111=>[1,2,2,1,1,1]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>1000111=>[1,4,1,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>0100111=>[2,3,1,1,1]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>0100111=>[2,3,1,1,1]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011=>[1,1,4,1,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1100111=>[1,1,3,1,1,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>1100111=>[1,1,3,1,1,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1101111=>[1,1,2,1,1,1,1]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>0010111=>[3,2,1,1,1]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>1010111=>[1,2,2,1,1,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>0001011=>[4,2,1,1]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>0011011=>[3,1,2,1,1]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>0011011=>[3,1,2,1,1]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>0111011=>[2,1,1,2,1,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011=>[1,3,2,1,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>0101011=>[2,2,2,1,1]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011=>[1,1,2,2,1,1]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>0111011=>[2,1,1,2,1,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0111011=>[2,1,1,2,1,1]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011=>[1,1,1,1,2,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>0000111=>[5,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>0001111=>[4,1,1,1,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>0010111=>[3,2,1,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>0001111=>[4,1,1,1,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>0011111=>[3,1,1,1,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>0100111=>[2,3,1,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>0101111=>[2,2,1,1,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>0010111=>[3,2,1,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>0110111=>[2,1,2,1,1,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>0001111=>[4,1,1,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>0011111=>[3,1,1,1,1,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>0101111=>[2,2,1,1,1,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>0011111=>[3,1,1,1,1,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1000111=>[1,4,1,1,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>1010111=>[1,2,2,1,1,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>0100111=>[2,3,1,1,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111=>[1,1,3,1,1,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>0010111=>[3,2,1,1,1]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>0110111=>[2,1,2,1,1,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1010111=>[1,2,2,1,1,1]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>0110111=>[2,1,2,1,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1110111=>[1,1,1,2,1,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>0001111=>[4,1,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>0011111=>[3,1,1,1,1,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>0101111=>[2,2,1,1,1,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>0011111=>[3,1,1,1,1,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1001111=>[1,3,1,1,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>1011111=>[1,2,1,1,1,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>0101111=>[2,2,1,1,1,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1101111=>[1,1,2,1,1,1,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>0011111=>[3,1,1,1,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>0111111=>[2,1,1,1,1,1,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>1011111=>[1,2,1,1,1,1,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>0111111=>[2,1,1,1,1,1,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111=>[1,1,1,1,1,1,1,1]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
searching the database
Sorry, this map was not found in the database.