Identifier
Mp00014: Binary trees to 132-avoiding permutationPermutations
Mp00252: Permutations restrictionPermutations
Mp00130: Permutations descent topsBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[]=> [.,[.,.]]=>[2,1]=>[1]=> [[.,.],.]=>[1,2]=>[1]=> [.,[.,[.,.]]]=>[3,2,1]=>[2,1]=>1 [.,[[.,.],.]]=>[2,3,1]=>[2,1]=>1 [[.,.],[.,.]]=>[3,1,2]=>[1,2]=>0 [[.,[.,.]],.]=>[2,1,3]=>[2,1]=>1 [[[.,.],.],.]=>[1,2,3]=>[1,2]=>0 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[3,2,1]=>11 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,2,1]=>11 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[2,3,1]=>01 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,1]=>11 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,1]=>01 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,2]=>01 [[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,1,2]=>01 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,1,3]=>10 [[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,3]=>00 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1]=>11 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1]=>01 [[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2]=>01 [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3]=>10 [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3]=>00 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[4,3,2,1]=>111 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,3,2,1]=>111 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[3,4,2,1]=>101 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,2,1]=>111 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,2,1]=>101 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[4,2,3,1]=>011 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[4,2,3,1]=>011 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[3,2,4,1]=>011 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[2,3,4,1]=>001 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,1]=>111 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,1]=>101 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[4,2,3,1]=>011 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,1]=>011 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,1]=>001 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,3,1,2]=>011 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,3,1,2]=>011 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[3,4,1,2]=>001 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,3,1,2]=>011 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,4,1,2]=>001 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,2,1,3]=>101 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,2,1,3]=>101 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,3]=>001 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[4,1,2,3]=>001 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[3,2,1,4]=>110 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[2,3,1,4]=>010 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,2,4]=>010 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,1,3,4]=>100 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,2,3,4]=>000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1]=>111 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1]=>101 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1]=>011 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1]=>011 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1]=>001 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[4,3,1,2]=>011 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2]=>001 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[4,2,1,3]=>101 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3]=>001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4]=>110 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4]=>010 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4]=>010 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4]=>100 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4]=>000 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>1111 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,4,3,2,1]=>1111 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[4,5,3,2,1]=>1101 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,3,2,1]=>1111 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,3,2,1]=>1101 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[5,3,4,2,1]=>1011 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[5,3,4,2,1]=>1011 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[4,3,5,2,1]=>1011 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[3,4,5,2,1]=>1001 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,2,1]=>1111 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,2,1]=>1101 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[5,3,4,2,1]=>1011 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,2,1]=>1011 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,2,1]=>1001 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[5,4,2,3,1]=>0111 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[5,4,2,3,1]=>0111 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[4,5,2,3,1]=>0101 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[5,4,2,3,1]=>0111 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[4,5,2,3,1]=>0101 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[5,3,2,4,1]=>0111 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[5,3,2,4,1]=>0111 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[5,2,3,4,1]=>0011 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[5,2,3,4,1]=>0011 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[4,3,2,5,1]=>0111 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[3,4,2,5,1]=>0011 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[4,2,3,5,1]=>0011 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[3,2,4,5,1]=>0101 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[2,3,4,5,1]=>0001 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,1]=>1111 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,1]=>1101 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[5,3,4,2,1]=>1011 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,1]=>1011 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,1]=>1001 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[5,4,2,3,1]=>0111 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[4,5,2,3,1]=>0101 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[5,3,2,4,1]=>0111 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[5,2,3,4,1]=>0011 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,1]=>0111 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,1]=>0011 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[4,2,3,5,1]=>0011 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,1]=>0101 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,1]=>0001 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,4,3,1,2]=>0111 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,4,3,1,2]=>0111 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[4,5,3,1,2]=>0101 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,4,3,1,2]=>0111 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[4,5,3,1,2]=>0101 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,3,4,1,2]=>0011 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,3,4,1,2]=>0011 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[4,3,5,1,2]=>0011 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,4,5,1,2]=>0001 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,4,3,1,2]=>0111 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[4,5,3,1,2]=>0101 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,3,4,1,2]=>0011 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[4,3,5,1,2]=>0011 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[3,4,5,1,2]=>0001 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,2,1,3]=>1011 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,2,1,3]=>1011 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[4,5,2,1,3]=>1001 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,2,1,3]=>1011 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[4,5,2,1,3]=>1001 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[5,4,1,2,3]=>0011 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[5,4,1,2,3]=>0011 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,1,2,3]=>0001 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[5,4,1,2,3]=>0011 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,1,2,3]=>0001 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,3,2,1,4]=>1101 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,3,2,1,4]=>1101 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,2,3,1,4]=>0101 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,2,3,1,4]=>0101 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[5,3,1,2,4]=>0101 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[5,3,1,2,4]=>0101 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[5,2,1,3,4]=>1001 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[5,2,1,3,4]=>1001 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,4]=>0001 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[5,1,2,3,4]=>0001 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[4,3,2,1,5]=>1110 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[3,4,2,1,5]=>1010 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[4,2,3,1,5]=>0110 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[3,2,4,1,5]=>0110 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[2,3,4,1,5]=>0010 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,3,1,2,5]=>0110 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,4,1,2,5]=>0010 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,2,1,3,5]=>1010 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,3,5]=>0010 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[3,2,1,4,5]=>1100 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[2,3,1,4,5]=>0100 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,2,4,5]=>0100 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,1,3,4,5]=>1000 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,2,3,4,5]=>0000 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1]=>1111 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1]=>1101 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,3,4,2,1]=>1011 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1]=>1011 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1]=>1001 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,4,2,3,1]=>0111 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[4,5,2,3,1]=>0101 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1]=>0111 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1]=>0011 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1]=>0111 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1]=>0011 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[4,2,3,5,1]=>0011 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1]=>0101 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1]=>0001 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[5,4,3,1,2]=>0111 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2]=>0101 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[5,3,4,1,2]=>0011 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,3,5,1,2]=>0011 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,4,5,1,2]=>0001 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[5,4,2,1,3]=>1011 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,5,2,1,3]=>1001 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[5,4,1,2,3]=>0011 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[4,5,1,2,3]=>0001 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[5,3,2,1,4]=>1101 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[5,2,3,1,4]=>0101 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[5,3,1,2,4]=>0101 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[5,2,1,3,4]=>1001 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4]=>0001 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5]=>1110 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5]=>1010 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5]=>0110 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5]=>0110 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5]=>0010 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,3,1,2,5]=>0110 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5]=>0010 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,2,1,3,5]=>1010 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5]=>0010 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5]=>1100 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5]=>0100 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5]=>0100 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5]=>1000 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5]=>0000 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[5,6,4,3,2,1]=>11101 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,4,3,2,1]=>11101 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[6,4,5,3,2,1]=>11011 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[6,4,5,3,2,1]=>11011 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[5,4,6,3,2,1]=>11011 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[4,5,6,3,2,1]=>11001 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,3,2,1]=>11101 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[6,4,5,3,2,1]=>11011 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,3,2,1]=>11011 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,3,2,1]=>11001 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[6,5,3,4,2,1]=>10111 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[6,5,3,4,2,1]=>10111 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[5,6,3,4,2,1]=>10101 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[6,5,3,4,2,1]=>10111 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[5,6,3,4,2,1]=>10101 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[6,4,3,5,2,1]=>10111 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[6,4,3,5,2,1]=>10111 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[6,3,4,5,2,1]=>10011 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[6,3,4,5,2,1]=>10011 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[5,4,3,6,2,1]=>10111 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[4,5,3,6,2,1]=>10011 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[5,3,4,6,2,1]=>10011 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[4,3,5,6,2,1]=>10101 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[3,4,5,6,2,1]=>10001 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,2,1]=>11101 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[6,4,5,3,2,1]=>11011 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,2,1]=>11011 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,2,1]=>11001 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[6,5,3,4,2,1]=>10111 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[5,6,3,4,2,1]=>10101 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[6,4,3,5,2,1]=>10111 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[6,3,4,5,2,1]=>10011 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,2,1]=>10111 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,2,1]=>10011 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[5,3,4,6,2,1]=>10011 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,2,1]=>10101 [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,2,1]=>10001 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[6,5,4,2,3,1]=>01111 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[6,5,4,2,3,1]=>01111 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[5,6,4,2,3,1]=>01101 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[6,5,4,2,3,1]=>01111 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[5,6,4,2,3,1]=>01101 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[6,4,5,2,3,1]=>01011 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[6,4,5,2,3,1]=>01011 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[5,4,6,2,3,1]=>01011 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[4,5,6,2,3,1]=>01001 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[6,5,4,2,3,1]=>01111 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[5,6,4,2,3,1]=>01101 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[6,4,5,2,3,1]=>01011 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[5,4,6,2,3,1]=>01011 [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,5,6,2,3,1]=>01001 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[6,5,3,2,4,1]=>01111 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[6,5,3,2,4,1]=>01111 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[5,6,3,2,4,1]=>01101 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[6,5,3,2,4,1]=>01111 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[5,6,3,2,4,1]=>01101 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[6,5,2,3,4,1]=>00111 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[6,5,2,3,4,1]=>00111 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[5,6,2,3,4,1]=>00101 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[6,5,2,3,4,1]=>00111 [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[5,6,2,3,4,1]=>00101 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[6,4,3,2,5,1]=>01111 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[6,4,3,2,5,1]=>01111 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[6,3,4,2,5,1]=>00111 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[6,3,4,2,5,1]=>00111 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[6,4,2,3,5,1]=>00111 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[6,4,2,3,5,1]=>00111 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[6,3,2,4,5,1]=>01011 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[6,3,2,4,5,1]=>01011 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[6,2,3,4,5,1]=>00011 [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[6,2,3,4,5,1]=>00011 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[5,4,3,2,6,1]=>01111 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[4,5,3,2,6,1]=>01011 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[5,3,4,2,6,1]=>00111 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[4,3,5,2,6,1]=>00111 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[3,4,5,2,6,1]=>00011 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[5,4,2,3,6,1]=>00111 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[4,5,2,3,6,1]=>00011 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[5,3,2,4,6,1]=>01011 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[5,2,3,4,6,1]=>00011 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[4,3,2,5,6,1]=>01101 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[3,4,2,5,6,1]=>00101 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[4,2,3,5,6,1]=>00101 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,1]=>01001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00001 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,1]=>11111 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,1]=>11101 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[6,4,5,3,2,1]=>11011 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,1]=>11011 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,1]=>11001 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[6,5,3,4,2,1]=>10111 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[5,6,3,4,2,1]=>10101 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[6,4,3,5,2,1]=>10111 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[6,3,4,5,2,1]=>10011 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,1]=>10111 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,1]=>10011 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[5,3,4,6,2,1]=>10011 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,1]=>10101 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,1]=>10001 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[6,5,4,2,3,1]=>01111 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[5,6,4,2,3,1]=>01101 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[6,4,5,2,3,1]=>01011 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[5,4,6,2,3,1]=>01011 [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,5,6,2,3,1]=>01001 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[6,5,3,2,4,1]=>01111 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[5,6,3,2,4,1]=>01101 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[6,5,2,3,4,1]=>00111 [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[5,6,2,3,4,1]=>00101 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[6,4,3,2,5,1]=>01111 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[6,3,4,2,5,1]=>00111 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[6,4,2,3,5,1]=>00111 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[6,3,2,4,5,1]=>01011 [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[6,2,3,4,5,1]=>00011 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,1]=>01111 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,1]=>01011 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[5,3,4,2,6,1]=>00111 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,1]=>00111 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,1]=>00011 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[5,4,2,3,6,1]=>00111 [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,5,2,3,6,1]=>00011 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[5,3,2,4,6,1]=>01011 [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[5,2,3,4,6,1]=>00011 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,1]=>01101 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,1]=>00101 [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[4,2,3,5,6,1]=>00101 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,1]=>01001 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,1]=>00001 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,5,4,3,1,2]=>01111 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,5,4,3,1,2]=>01111 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[5,6,4,3,1,2]=>01101 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,5,4,3,1,2]=>01111 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[5,6,4,3,1,2]=>01101 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,4,5,3,1,2]=>01011 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,4,5,3,1,2]=>01011 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[5,4,6,3,1,2]=>01011 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[4,5,6,3,1,2]=>01001 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,5,4,3,1,2]=>01111 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[5,6,4,3,1,2]=>01101 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,4,5,3,1,2]=>01011 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[5,4,6,3,1,2]=>01011 [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,5,6,3,1,2]=>01001 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,5,3,4,1,2]=>00111 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,5,3,4,1,2]=>00111 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[5,6,3,4,1,2]=>00101 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,5,3,4,1,2]=>00111 [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[5,6,3,4,1,2]=>00101 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,4,3,5,1,2]=>00111 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,4,3,5,1,2]=>00111 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,3,4,5,1,2]=>00011 [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,3,4,5,1,2]=>00011 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[5,4,3,6,1,2]=>00111 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[4,5,3,6,1,2]=>00011 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[5,3,4,6,1,2]=>00011 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[4,3,5,6,1,2]=>00101 [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[3,4,5,6,1,2]=>00001 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,5,4,3,1,2]=>01111 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[5,6,4,3,1,2]=>01101 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,4,5,3,1,2]=>01011 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[5,4,6,3,1,2]=>01011 [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,5,6,3,1,2]=>01001 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,5,3,4,1,2]=>00111 [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[5,6,3,4,1,2]=>00101 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,4,3,5,1,2]=>00111 [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,3,4,5,1,2]=>00011 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[5,4,3,6,1,2]=>00111 [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,5,3,6,1,2]=>00011 [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[5,3,4,6,1,2]=>00011 [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,3,5,6,1,2]=>00101 [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[3,4,5,6,1,2]=>00001 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,4,2,1,3]=>10111 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,4,2,1,3]=>10111 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[5,6,4,2,1,3]=>10101 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,4,2,1,3]=>10111 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[5,6,4,2,1,3]=>10101 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,4,5,2,1,3]=>10011 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,4,5,2,1,3]=>10011 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[5,4,6,2,1,3]=>10011 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[4,5,6,2,1,3]=>10001 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,4,2,1,3]=>10111 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[5,6,4,2,1,3]=>10101 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,4,5,2,1,3]=>10011 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[5,4,6,2,1,3]=>10011 [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,5,6,2,1,3]=>10001 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[6,5,4,1,2,3]=>00111 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[6,5,4,1,2,3]=>00111 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,4,1,2,3]=>00101 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[6,5,4,1,2,3]=>00111 [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,4,1,2,3]=>00101 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[6,4,5,1,2,3]=>00011 [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[6,4,5,1,2,3]=>00011 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,4,6,1,2,3]=>00011 [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[4,5,6,1,2,3]=>00001 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[6,5,4,1,2,3]=>00111 [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,4,1,2,3]=>00101 [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[6,4,5,1,2,3]=>00011 [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,4,6,1,2,3]=>00011 [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,5,6,1,2,3]=>00001 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,3,2,1,4]=>11011 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,3,2,1,4]=>11011 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[5,6,3,2,1,4]=>11001 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,3,2,1,4]=>11011 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[5,6,3,2,1,4]=>11001 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,5,2,3,1,4]=>01011 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,5,2,3,1,4]=>01011 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[5,6,2,3,1,4]=>01001 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,5,2,3,1,4]=>01011 [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[5,6,2,3,1,4]=>01001 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[6,5,3,1,2,4]=>01011 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[6,5,3,1,2,4]=>01011 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,3,1,2,4]=>01001 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[6,5,3,1,2,4]=>01011 [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,3,1,2,4]=>01001 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[6,5,2,1,3,4]=>10011 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[6,5,2,1,3,4]=>10011 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,6,2,1,3,4]=>10001 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[6,5,2,1,3,4]=>10011 [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,6,2,1,3,4]=>10001 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[6,5,1,2,3,4]=>00011 [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[6,5,1,2,3,4]=>00011 [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[5,6,1,2,3,4]=>00001 [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[6,5,1,2,3,4]=>00011 [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[5,6,1,2,3,4]=>00001 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,4,3,2,1,5]=>11101 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,4,3,2,1,5]=>11101 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,3,4,2,1,5]=>10101 [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,3,4,2,1,5]=>10101 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,2,3,1,5]=>01101 [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,2,3,1,5]=>01101 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,3,2,4,1,5]=>01101 [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,3,2,4,1,5]=>01101 [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,2,3,4,1,5]=>00101 [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,2,3,4,1,5]=>00101 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[6,4,3,1,2,5]=>01101 [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[6,4,3,1,2,5]=>01101 [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[6,3,4,1,2,5]=>00101 [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[6,3,4,1,2,5]=>00101 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[6,4,2,1,3,5]=>10101 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[6,4,2,1,3,5]=>10101 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[6,4,1,2,3,5]=>00101 [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[6,4,1,2,3,5]=>00101 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[6,3,2,1,4,5]=>11001 [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[6,3,2,1,4,5]=>11001 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[6,2,3,1,4,5]=>01001 [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[6,2,3,1,4,5]=>01001 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[6,3,1,2,4,5]=>01001 [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[6,3,1,2,4,5]=>01001 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[6,2,1,3,4,5]=>10001 [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[6,2,1,3,4,5]=>10001 [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001 [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[4,5,3,2,1,6]=>11010 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[5,3,4,2,1,6]=>10110 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[4,3,5,2,1,6]=>10110 [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[3,4,5,2,1,6]=>10010 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[5,4,2,3,1,6]=>01110 [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[4,5,2,3,1,6]=>01010 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[5,3,2,4,1,6]=>01110 [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[5,2,3,4,1,6]=>00110 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[4,3,2,5,1,6]=>01110 [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[3,4,2,5,1,6]=>00110 [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[4,2,3,5,1,6]=>00110 [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[3,2,4,5,1,6]=>01010 [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[2,3,4,5,1,6]=>00010 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,4,3,1,2,6]=>01110 [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[4,5,3,1,2,6]=>01010 [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,3,4,1,2,6]=>00110 [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[4,3,5,1,2,6]=>00110 [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[3,4,5,1,2,6]=>00010 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,2,1,3,6]=>10110 [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[4,5,2,1,3,6]=>10010 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[5,4,1,2,3,6]=>00110 [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,1,2,3,6]=>00010 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,3,2,1,4,6]=>11010 [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,2,3,1,4,6]=>01010 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[5,3,1,2,4,6]=>01010 [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[5,2,1,3,4,6]=>10010 [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,4,6]=>00010 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100 [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[3,4,2,1,5,6]=>10100 [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[4,2,3,1,5,6]=>01100 [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[3,2,4,1,5,6]=>01100 [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[2,3,4,1,5,6]=>00100 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,3,1,2,5,6]=>01100 [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[3,4,1,2,5,6]=>00100 [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,2,1,3,5,6]=>10100 [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,3,5,6]=>00100 [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000 [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[2,3,1,4,5,6]=>01000 [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,2,4,5,6]=>01000 [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000 [[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1]=>11111 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1]=>11101 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,4,5,3,2,1]=>11011 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1]=>11011 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1]=>11001 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1]=>10111 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[5,6,3,4,2,1]=>10101 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,4,3,5,2,1]=>10111 [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,3,4,5,2,1]=>10011 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1]=>10111 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1]=>10011 [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[5,3,4,6,2,1]=>10011 [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1]=>10101 [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1]=>10001 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,5,4,2,3,1]=>01111 [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[5,6,4,2,3,1]=>01101 [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1]=>01011 [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[5,4,6,2,3,1]=>01011 [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,5,6,2,3,1]=>01001 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,5,3,2,4,1]=>01111 [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[5,6,3,2,4,1]=>01101 [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,5,2,3,4,1]=>00111 [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[5,6,2,3,4,1]=>00101 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1]=>01111 [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,3,4,2,5,1]=>00111 [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,4,2,3,5,1]=>00111 [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1]=>01011 [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1]=>00011 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1]=>01111 [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1]=>01011 [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[5,3,4,2,6,1]=>00111 [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1]=>00111 [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1]=>00011 [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[5,4,2,3,6,1]=>00111 [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,5,2,3,6,1]=>00011 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[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[6,4,3,5,1,2]=>00111 [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[6,3,4,5,1,2]=>00011 [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,4,3,6,1,2]=>00111 [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,5,3,6,1,2]=>00011 [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,3,4,6,1,2]=>00011 [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,3,5,6,1,2]=>00101 [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[3,4,5,6,1,2]=>00001 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[6,5,4,2,1,3]=>10111 [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,6,4,2,1,3]=>10101 [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[6,4,5,2,1,3]=>10011 [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3]=>10011 [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,5,6,2,1,3]=>10001 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[6,5,4,1,2,3]=>00111 [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[5,6,4,1,2,3]=>00101 [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[6,4,5,1,2,3]=>00011 [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[5,4,6,1,2,3]=>00011 [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3]=>00001 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[6,5,3,2,1,4]=>11011 [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,6,3,2,1,4]=>11001 [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[6,5,2,3,1,4]=>01011 [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,6,2,3,1,4]=>01001 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[6,5,3,1,2,4]=>01011 [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[5,6,3,1,2,4]=>01001 [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[6,5,2,1,3,4]=>10011 [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[5,6,2,1,3,4]=>10001 [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[6,5,1,2,3,4]=>00011 [[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[5,6,1,2,3,4]=>00001 [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[6,4,3,2,1,5]=>11101 [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[6,3,4,2,1,5]=>10101 [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[6,4,2,3,1,5]=>01101 [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[6,3,2,4,1,5]=>01101 [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[6,2,3,4,1,5]=>00101 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[6,4,3,1,2,5]=>01101 [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[6,3,4,1,2,5]=>00101 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[6,4,2,1,3,5]=>10101 [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[6,4,1,2,3,5]=>00101 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[6,3,2,1,4,5]=>11001 [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[6,2,3,1,4,5]=>01001 [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[6,3,1,2,4,5]=>01001 [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[6,2,1,3,4,5]=>10001 [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5]=>00001 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6]=>11110 [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6]=>11010 [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,3,4,2,1,6]=>10110 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6]=>10110 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6]=>10010 [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,4,2,3,1,6]=>01110 [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,5,2,3,1,6]=>01010 [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6]=>01110 [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6]=>00110 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6]=>01110 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6]=>00110 [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[4,2,3,5,1,6]=>00110 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6]=>01010 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6]=>00010 [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[5,4,3,1,2,6]=>01110 [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6]=>01010 [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[5,3,4,1,2,6]=>00110 [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,3,5,1,2,6]=>00110 [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4,5,1,2,6]=>00010 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[5,4,2,1,3,6]=>10110 [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,5,2,1,3,6]=>10010 [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[5,4,1,2,3,6]=>00110 [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,5,1,2,3,6]=>00010 [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[5,3,2,1,4,6]=>11010 [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,2,3,1,4,6]=>01010 [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[5,3,1,2,4,6]=>01010 [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[5,2,1,3,4,6]=>10010 [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6]=>00010 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6]=>11100 [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6]=>10100 [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6]=>01100 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6]=>01100 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6]=>00100 [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,3,1,2,5,6]=>01100 [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6]=>00100 [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,2,1,3,5,6]=>10100 [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6]=>00100 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6]=>11000 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6]=>01000 [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6]=>01000 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6]=>10000 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6]=>00000 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>111101 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>111011 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[7,5,6,4,3,2,1]=>111011 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,5,7,4,3,2,1]=>111011 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,4,3,2,1]=>111001 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>110111 [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>110111 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[6,7,4,5,3,2,1]=>110101 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,3,2,1]=>111011 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[7,6,4,5,3,2,1]=>110111 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[7,5,4,6,3,2,1]=>110111 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[7,4,5,6,3,2,1]=>110011 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,3,2,1]=>110001 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[7,6,5,3,4,2,1]=>101111 [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[7,6,5,3,4,2,1]=>101111 [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[6,7,5,3,4,2,1]=>101101 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[7,5,6,3,4,2,1]=>101011 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[5,6,7,3,4,2,1]=>101001 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[6,7,3,4,5,2,1]=>100101 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[7,5,4,3,6,2,1]=>101111 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[6,4,5,7,3,2,1]=>110011 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,2,1]=>110101 [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[7,6,5,3,4,2,1]=>101111 [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[7,6,4,3,5,2,1]=>101111 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[7,6,3,4,5,2,1]=>100111 [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[6,3,4,5,7,2,1]=>100011 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,2,1]=>101001 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[7,6,5,4,2,3,1]=>011111 [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[7,6,5,4,2,3,1]=>011111 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[6,7,5,4,2,3,1]=>011101 [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>011011 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[5,6,7,4,2,3,1]=>011001 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[7,6,4,5,2,3,1]=>010111 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[6,7,4,5,2,3,1]=>010101 [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[4,5,6,7,2,3,1]=>010001 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[7,6,5,3,2,4,1]=>011111 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[6,5,7,3,2,4,1]=>011011 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[5,6,7,3,2,4,1]=>011001 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[7,6,5,2,3,4,1]=>001111 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[6,7,5,2,3,4,1]=>001101 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[5,6,7,2,3,4,1]=>001001 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[5,6,7,2,3,4,1]=>001001 [.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>010011 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,1]=>111111 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,7,5,4,3,2,1]=>111101 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,5,7,4,3,2,1]=>111011 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[6,4,5,7,3,2,1]=>110011 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,1]=>101111 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,1]=>100111 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[6,5,3,4,7,2,1]=>100111 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[7,6,5,4,2,3,1]=>011111 [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[6,7,4,5,2,3,1]=>010101 [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[6,4,5,7,2,3,1]=>010011 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[4,5,6,7,2,3,1]=>010001 [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[7,6,5,3,2,4,1]=>011111 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[7,6,5,2,3,4,1]=>001111 [.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[6,7,2,3,4,5,1]=>000101 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,1]=>011101 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,5,2,6,7,1]=>000101 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[5,2,3,4,6,7,1]=>000101 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,1]=>011001 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,1]=>001001 [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[4,2,3,5,6,7,1]=>001001 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,1]=>010001 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,1]=>000001 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>011111 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>011111 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>011101 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[7,5,6,4,3,1,2]=>011011 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[6,5,7,4,3,1,2]=>011011 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[5,6,7,4,3,1,2]=>011001 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[7,6,4,5,3,1,2]=>010111 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,6,4,5,3,1,2]=>010111 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[4,5,6,7,3,1,2]=>010001 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,6,5,3,4,1,2]=>001111 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,6,5,3,4,1,2]=>001111 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[6,7,5,3,4,1,2]=>001101 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[6,5,7,3,4,1,2]=>001011 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[5,6,7,3,4,1,2]=>001001 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,5,4,3,6,1,2]=>001111 [[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,4,5,3,6,1,2]=>000111 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,5,3,4,6,1,2]=>000111 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,4,3,5,6,1,2]=>001011 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[7,3,4,5,6,1,2]=>000011 [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[4,3,5,6,7,1,2]=>001001 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[3,4,5,6,7,1,2]=>000001 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,6,5,4,3,1,2]=>011111 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[6,5,7,4,3,1,2]=>011011 [[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[5,6,7,4,3,1,2]=>011001 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[6,7,4,5,3,1,2]=>010101 [[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[5,6,4,7,3,1,2]=>010011 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[5,4,6,7,3,1,2]=>010101 [[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[5,4,6,3,7,1,2]=>000111 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[5,6,3,4,7,1,2]=>000011 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[6,4,3,5,7,1,2]=>001011 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[6,3,4,5,7,1,2]=>000011 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,1,2]=>001101 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[4,5,3,6,7,1,2]=>000101 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[4,3,5,6,7,1,2]=>001001 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[3,4,5,6,7,1,2]=>000001 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>101111 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>101111 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[5,6,7,4,2,1,3]=>101001 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[4,5,6,7,2,1,3]=>100001 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[7,6,5,4,1,2,3]=>001111 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,5,4,1,2,3]=>001101 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>001001 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,5,7,4,1,2,3]=>001011 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[5,6,7,4,1,2,3]=>001001 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[7,6,4,5,1,2,3]=>000111 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[6,7,4,5,1,2,3]=>000101 [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[7,4,5,6,1,2,3]=>000011 [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[7,4,5,6,1,2,3]=>000011 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,7,4,5,1,2,3]=>000101 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,5,4,7,1,2,3]=>000111 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[4,5,6,7,1,2,3]=>000001 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,3,2,1,4]=>110111 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,5,6,3,2,1,4]=>110011 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,4]=>110111 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[5,6,7,3,2,1,4]=>110001 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,6,5,2,3,1,4]=>010111 [[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,2,3,1,4]=>010011 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[6,7,5,2,3,1,4]=>010101 [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,2,3,1,4]=>010011 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[5,6,7,2,3,1,4]=>010001 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[7,6,5,3,1,2,4]=>010111 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[7,5,6,3,1,2,4]=>010011 [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,3,1,2,4]=>010101 [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[7,5,6,3,1,2,4]=>010011 [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[5,6,7,3,1,2,4]=>010001 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>100111 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>100111 [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,7,5,2,1,3,4]=>100101 [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[7,5,6,2,1,3,4]=>100011 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,2,1,3,4]=>100011 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[5,6,7,2,1,3,4]=>100001 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[6,5,7,1,2,3,4]=>000011 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,1,2,3,4]=>000001 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[6,5,7,1,2,3,4]=>000011 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,1,2,3,4]=>000001 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,4,3,2,1,5]=>111011 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[6,7,4,3,2,1,5]=>111001 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,3,4,2,1,5]=>101011 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[6,7,3,4,2,1,5]=>101001 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,6,4,2,3,1,5]=>011011 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[6,7,4,2,3,1,5]=>011001 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,6,3,2,4,1,5]=>011011 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[6,7,3,2,4,1,5]=>011001 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,6,2,3,4,1,5]=>001011 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[6,7,2,3,4,1,5]=>001001 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[7,6,4,3,1,2,5]=>011011 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,7,4,3,1,2,5]=>011001 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[7,6,3,4,1,2,5]=>001011 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,3,4,1,2,5]=>001001 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[7,6,4,2,1,3,5]=>101011 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,7,4,2,1,3,5]=>101001 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[7,6,4,1,2,3,5]=>001011 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[6,7,4,1,2,3,5]=>001001 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[7,6,3,2,1,4,5]=>110011 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,7,3,2,1,4,5]=>110001 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[7,6,2,3,1,4,5]=>010011 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,7,2,3,1,4,5]=>010001 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[7,6,3,1,2,4,5]=>010011 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[6,7,3,1,2,4,5]=>010001 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[7,6,2,1,3,4,5]=>100011 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[6,7,2,1,3,4,5]=>100001 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>000001 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>000001 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,5,4,3,2,1,6]=>111101 [[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,4,5,2,3,1,6]=>010101 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,3,4,2,5,1,6]=>001101 [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[7,5,4,2,1,3,6]=>101101 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[7,5,4,1,2,3,6]=>001101 [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[7,4,5,1,2,3,6]=>000101 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>100101 [[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>100101 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>000101 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>000101 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>111001 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>111001 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[7,3,2,4,1,5,6]=>011001 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[7,2,3,4,1,5,6]=>001001 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[7,3,4,1,2,5,6]=>001001 [[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[7,4,2,1,3,5,6]=>101001 [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[7,4,1,2,3,5,6]=>001001 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>100001 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>110010 [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[6,5,4,3,1,2,7]=>011110 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>001010 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,3,5,6,1,2,7]=>001010 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[3,4,5,6,1,2,7]=>000010 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,5,4,2,1,3,7]=>101110 [[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[6,4,5,1,2,3,7]=>000110 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,5,2,3,1,4,7]=>010110 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[5,6,2,3,1,4,7]=>010010 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,6,2,1,3,4,7]=>100010 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[6,5,1,2,3,4,7]=>000110 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[5,6,1,2,3,4,7]=>000010 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,4,3,2,1,5,7]=>111010 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,3,4,2,1,5,7]=>101010 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[6,4,2,1,3,5,7]=>101010 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>001000 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>001000 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000 [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000 [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>010000 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1]=>111111 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1]=>111101 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1]=>111011 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1]=>111001 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,4,5,3,2,1]=>110111 [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,4,5,6,3,2,1]=>110011 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1]=>110111 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,5,6,3,4,2,1]=>101011 [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[5,6,7,3,4,2,1]=>101001 [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,5,2,1]=>101111 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1]=>100111 [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,5,4,3,6,2,1]=>101111 [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[6,7,5,4,2,3,1]=>011101 [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[5,6,7,4,2,3,1]=>011001 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,6,4,5,2,3,1]=>010111 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[6,7,4,5,2,3,1]=>010101 [[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,4,5,6,2,3,1]=>010011 [[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[5,6,4,7,2,3,1]=>010011 [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[6,5,7,3,2,4,1]=>011011 [[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[5,6,7,3,2,4,1]=>011001 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,6,5,2,3,4,1]=>001111 [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[6,7,5,2,3,4,1]=>001101 [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,5,6,2,3,4,1]=>001011 [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[6,5,7,2,3,4,1]=>001011 [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[5,6,7,2,3,4,1]=>001001 [[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[6,7,3,4,2,5,1]=>001101 [[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1]=>000111 [[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[5,6,3,4,2,7,1]=>001011 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1]=>000111 [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1]=>011101 [[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[3,2,4,5,6,7,1]=>010001 [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,1]=>000001 [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[7,6,5,4,3,1,2]=>011111 [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[7,5,6,4,3,1,2]=>011011 [[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[7,4,5,6,3,1,2]=>010011 [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[7,6,5,4,2,1,3]=>101111 [[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3]=>101011 [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[7,5,4,6,2,1,3]=>100111 [[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[7,4,5,6,2,1,3]=>100011 [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[7,6,5,4,1,2,3]=>001111 [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3]=>001001 [[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[7,4,5,6,1,2,3]=>000011 [[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,4,7,1,2,3]=>000011 [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,4,6,7,1,2,3]=>000101 [[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4]=>010001 [[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,6,7,2,1,3,4]=>100001 [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4]=>000111 [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[6,7,5,1,2,3,4]=>000101 [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[7,5,6,1,2,3,4]=>000011 [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[6,5,7,1,2,3,4]=>000011 [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,4]=>000001 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[7,6,4,3,2,1,5]=>111011 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[7,6,4,3,1,2,5]=>011011 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[6,7,1,2,3,4,5]=>000001 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[7,5,3,1,2,4,6]=>010101 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[7,5,1,2,3,4,6]=>000101 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[7,4,3,2,1,5,6]=>111001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[7,3,1,2,4,5,6]=>010001 [[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[7,2,1,3,4,5,6]=>100001 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6]=>000001 [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7]=>111110 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7]=>011110 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7]=>010110 [[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[4,2,3,5,6,1,7]=>001010 [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,3,4,5,6,1,7]=>000010 [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7]=>011010 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,4,6,3,1,2,7]=>010110 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7]=>001010 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,4,3,6,1,2,7]=>001110 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,6,4,2,1,3,7]=>101010 [[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7]=>100110 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7]=>000010 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,6,3,2,1,4,7]=>110010 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[6,4,3,2,1,5,7]=>111010 [[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[6,4,3,1,2,5,7]=>011010 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[6,4,1,2,3,5,7]=>001010 [[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[6,2,3,1,4,5,7]=>010010 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7]=>000010 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7]=>111100 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[4,5,2,3,1,6,7]=>010100 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7]=>001100 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7]=>000100 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[5,3,1,2,4,6,7]=>010100 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7]=>000100 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7]=>111000 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7]=>011000 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7]=>001000 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7]=>001000 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7]=>001000 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7]=>110000 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7]=>010000 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7]=>100000 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7]=>000000 [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1]=>1111101 [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,1]=>0000001 [[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8]=>0000000 [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1]=>11110001 [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[3,4,5,6,7,8,1,2]=>0000001 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,1]=>00000001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9]=>00000000 [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,1]=>1111111 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[8,6,7,5,4,3,2,1]=>1111011 [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>1110111 [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[8,7,6,4,5,3,2,1]=>1101111 [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[8,7,6,5,3,4,2,1]=>1011111 [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[8,7,6,5,4,2,3,1]=>0111111 [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[8,7,6,5,4,3,1,2]=>0111111 [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1]=>11111111 [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,7,8,5,6,3,4,1,2]=>00101011 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000 [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,1]=>0100001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000 [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>0100000 [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000 [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[4,2,3,5,6,7,8,1]=>0010001 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,4,2,5,6,7,8,1]=>0010001 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,2,4,5,6,7,8,9,1]=>01000001 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,3,4,5,6,7,8,9,10,1]=>000000001 [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001 [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[7,8,1,2,3,4,5,6]=>0000001 [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[6,7,8,1,2,3,4,5]=>0000001 [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001 [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001 [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[8,9,1,2,3,4,5,6,7]=>00000001 [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[7,8,9,1,2,3,4,5,6]=>00000001 [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,1,2,3,4,5]=>00000001 [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[3,4,5,6,7,8,9,1,2]=>00000001 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,1,2]=>0111111 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,8,6,5,4,3,2,1]=>1111101 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,1,2]=>01111111 [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1]=>111111111 [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[8,9,7,6,5,4,3,2,1]=>11111101 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,6,8,5,4,3,2,1]=>1111011 [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[8,7,6,5,4,1,2,3]=>0011111 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8]=>1111110 [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8]=>1111100 [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8]=>1111000 [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8]=>1110000 [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8]=>1100000 [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8]=>1000000 [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9]=>11111110 [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9]=>11111100 [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9]=>11111000 [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9]=>11110000 [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9]=>11100000 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9]=>11000000 [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9]=>10000000 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10]=>100000000 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,1]=>0000001 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,1,8]=>0000010 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,1]=>00000001 [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8]=>0000010 [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7]=>0000001 [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8]=>00000001 [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,1,2,3]=>00111111 [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001 [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[8,7,1,2,3,4,5,6]=>0000011 [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[8,7,6,1,2,3,4,5]=>0000111 [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[8,7,6,5,1,2,3,4]=>0001111 [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[9,8,1,2,3,4,5,6,7]=>00000011 [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[9,8,7,1,2,3,4,5,6]=>00000111 [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[9,8,7,6,1,2,3,4,5]=>00001111 [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,1,2,3,4]=>00011111 [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8]=>0010000
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.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
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.