Identifier
Mp00012: Binary trees to Dyck path: up step, left tree, down step, right treeDyck paths
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00114: Permutations connectivity setBinary words
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1
[.,.]=>[1,0]=>[1]=> [.,[.,.]]=>[1,0,1,0]=>[1,2]=>1 [[.,.],.]=>[1,1,0,0]=>[2,1]=>0 [.,[.,[.,.]]]=>[1,0,1,0,1,0]=>[1,2,3]=>11 [.,[[.,.],.]]=>[1,0,1,1,0,0]=>[1,3,2]=>10 [[.,.],[.,.]]=>[1,1,0,0,1,0]=>[2,1,3]=>01 [[.,[.,.]],.]=>[1,1,0,1,0,0]=>[2,3,1]=>00 [[[.,.],.],.]=>[1,1,1,0,0,0]=>[3,2,1]=>00 [.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>111 [.,[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>110 [.,[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>101 [.,[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>100 [.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>100 [[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>011 [[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>010 [[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>001 [[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>001 [[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>000 [[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>000 [[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>000 [[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>[4,2,3,1]=>000 [[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>000 [.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>1111 [.,[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>1110 [.,[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>1101 [.,[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>1100 [.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>1100 [.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>1011 [.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>1010 [.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>1001 [.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>1001 [.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>1000 [.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>1000 [.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>1000 [.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>1000 [.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>1000 [[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>0111 [[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>0110 [[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>0101 [[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>0100 [[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>0100 [[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0011 [[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0010 [[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>0011 [[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>0010 [[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0001 [[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>0001 [[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>0001 [[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>0001 [[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>0001 [[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0000 [[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>0000 [[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>0000 [[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>0000 [[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>0000 [[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>0000 [[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>0000 [[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>0000 [[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>0000 [[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>0000 [[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>0000 [[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>0000 [[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>0000 [[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>0000 [.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>11111 [.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>11110 [.,[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>11101 [.,[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>11100 [.,[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>11100 [.,[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>11011 [.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>11010 [.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>11001 [.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>11001 [.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>11000 [.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>11000 [.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>11000 [.,[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>11000 [.,[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>11000 [.,[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>10111 [.,[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>10110 [.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>10101 [.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>10100 [.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>10100 [.,[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>10011 [.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>10010 [.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>10011 [.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>10010 [.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>10001 [.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>10001 [.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>10001 [.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>10001 [.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>10001 [.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>10000 [.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>10000 [.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>10000 [.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>10000 [.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>10000 [.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>10000 [.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>10000 [.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>10000 [.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>10000 [.,[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>10000 [.,[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>10000 [.,[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>10000 [.,[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>10000 [.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>10000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>01111 [[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>01110 [[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>01101 [[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>01100 [[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>01100 [[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>01011 [[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>01010 [[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>01001 [[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>01001 [[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>01000 [[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>01000 [[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>01000 [[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>01000 [[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>01000 [[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>00111 [[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>00110 [[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>00101 [[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>00100 [[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>00100 [[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>00111 [[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>00110 [[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>00101 [[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>00100 [[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>00100 [[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>00011 [[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>00010 [[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>00011 [[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>00010 [[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>00011 [[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>00010 [[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>00011 [[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>00010 [[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>00011 [[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>00010 [[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>00001 [[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>00001 [[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>00001 [[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>00001 [[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>00001 [[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>00001 [[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>00001 [[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>00001 [[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>00001 [[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>00001 [[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>00001 [[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>00001 [[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>00001 [[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>00001 [[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>00000 [[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>00000 [[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>00000 [[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>00000 [[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>00000 [[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>00000 [[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>00000 [[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>00000 [[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>00000 [[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>00000 [[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>00000 [[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>00000 [[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>00000 [[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>00000 [[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>00000 [[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>00000 [[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>00000 [[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>00000 [[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>00000 [[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>00000 [[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>00000 [[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>00000 [[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>00000 [[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>00000 [[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>00000 [[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>00000 [[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>00000 [[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>00000 [[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>00000 [[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>00000 [[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>00000 [[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>00000 [[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>00000 [[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>00000 [[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>00000 [[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>00000 [[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>00000 [[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>00000 [[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>00000 [[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>00000 [[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>00000 [[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>00000 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>111111 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>111110 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>111101 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>111100 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>111100 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>111011 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>111010 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>111001 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>111001 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>111000 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>111000 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>111000 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>111000 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>111000 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>110111 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>110110 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>110101 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>110100 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>110100 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>110011 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>110010 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>110011 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>110010 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>110001 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>110001 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>110001 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>110001 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>110001 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>110000 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>110000 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>110000 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>110000 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>110000 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>110000 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>110000 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>110000 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>110000 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>110000 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>110000 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>110000 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>110000 [.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>110000 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>101111 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>101110 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>101101 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>101100 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>101100 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>101011 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>101010 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>101001 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>101001 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>101000 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>101000 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>101000 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>101000 [.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>101000 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>100111 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>100110 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>100101 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>100100 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>100100 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>100111 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>100110 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>100101 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>100100 [.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>100100 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>100011 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>100010 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>100011 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>100010 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>100011 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>100010 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>100011 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>100010 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>100011 [.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>100010 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>100001 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>100001 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>100001 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>100001 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>100001 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>100001 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>100001 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>100001 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>100001 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>100001 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>100001 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>100001 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>100001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>100001 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>100000 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>100000 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>100000 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>100000 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>100000 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>100000 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>100000 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>100000 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>100000 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>100000 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>100000 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>100000 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>100000 [.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>100000 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>100000 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>100000 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>100000 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>100000 [.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>100000 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>100000 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>100000 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>100000 [.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>100000 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>100000 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>100000 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>100000 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>100000 [.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>100000 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>100000 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>100000 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>100000 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>100000 [.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>100000 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>100000 [.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>100000 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>100000 [.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>100000 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>100000 [.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>100000 [.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>100000 [.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>100000 [.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>100000 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>011111 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>011110 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>011101 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>011100 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>011100 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>011011 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>011010 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>011001 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>011001 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>011000 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>011000 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>011000 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>011000 [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>011000 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>010111 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>010110 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>010101 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>010100 [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>010100 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>010011 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>010010 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>010011 [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>010010 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>010001 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>010001 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>010001 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>010001 [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>010001 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>010000 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>010000 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>010000 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>010000 [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>010000 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>010000 [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>010000 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>010000 [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>010000 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>010000 [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>010000 [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>010000 [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>010000 [[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>010000 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>001111 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>001110 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>001101 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>001100 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>001100 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>001011 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>001010 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>001001 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>001001 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>001000 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>001000 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>001000 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>001000 [[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>001000 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>001111 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>001110 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>001101 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>001100 [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>001100 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>001011 [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>001010 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>001001 [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>001001 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>001000 [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>001000 [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>001000 [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>001000 [[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>001000 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>000111 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>000110 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>000101 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>000100 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>000100 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>000111 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>000110 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>000101 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>000100 [[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>000100 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>000111 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>000110 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>000101 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>000100 [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>000100 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>000111 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>000110 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>000101 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>000100 [[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>000100 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>000111 [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>000110 [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>000101 [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>000100 [[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>000100 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>000011 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>000010 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>000011 [[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>000010 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>000011 [[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>000010 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>000011 [[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>000010 [[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>000011 [[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>000010 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>000011 [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>000010 [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>000011 [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>000010 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>000011 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>000010 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>000011 [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>000010 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>000011 [[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>000010 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>000011 [[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>000010 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>000011 [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>000010 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>000011 [[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>000010 [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>000011 [[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>000010 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>000001 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>000001 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>000001 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>000001 [[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>000001 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>000001 [[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>000001 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>000001 [[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>000001 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>000001 [[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>000001 [[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>000001 [[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>000001 [[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>000001 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>000001 [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>000001 [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>000001 [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>000001 [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>000001 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>000001 [[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>000001 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>000001 [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>000001 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>000001 [[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>000001 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>000001 [[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>000001 [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>000001 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>000001 [[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>000001 [[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>000001 [[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>000001 [[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>000001 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>000001 [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>000001 [[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>000001 [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>000001 [[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>000001 [[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>000001 [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>000001 [[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>000001 [[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>000001 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>000000 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>000000 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>000000 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>000000 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>000000 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>000000 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>000000 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>000000 [[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>000000 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>000000 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>000000 [[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>000000 [[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>000000 [[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>000000 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>000000 [[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>000000 [[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>000000 [[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>000000 [[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>000000 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>000000 [[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>000000 [[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>000000 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[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>1111111 [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>1111110 [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>1111101 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>1111100 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>1111100 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>1111011 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>1111010 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>1111001 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>1111001 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>1111000 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>1111000 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>1111000 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,8,6,7,5]=>1111000 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>1111000 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>1110111 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>1110101 [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>1110100 [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>1110100 [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>1110011 [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>1110010 [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>1110010 [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>1110001 [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>1110001 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>1110001 [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,7,5,6,4,8]=>1110001 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>1110001 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>1110000 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>1110000 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>1110000 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,8,6,7,4]=>1110000 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>1110000 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>1110000 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>1110000 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,7,5,6,8,4]=>1110000 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>1110000 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,8,5,6,7,4]=>1110000 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,8,5,7,6,4]=>1110000 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,8,6,5,7,4]=>1110000 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,8,6,7,5,4]=>1110000 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>1110000 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>1101111 [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>1101110 [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>1101100 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>1101011 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>1101010 [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>1101001 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>1101000 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>1101000 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>1101000 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>1100100 [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>1100110 [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>1100100 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>1100011 [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,6,4,5,3,7,8]=>1100011 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>1100011 [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>1100001 [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,8,6,7,3]=>1100000 [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>1100000 [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>1100000 [.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,8,6,5,7,3]=>1100000 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>1100000 [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>1100000 [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,8,6,7,3]=>1100000 [.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>1100000 [.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>1100000 [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,7,5,4,6,8,3]=>1100000 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,8,4,5,6,7,3]=>1100000 [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,8,5,4,6,7,3]=>1100000 [.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,8,5,4,7,6,3]=>1100000 [.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>1100000 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>1011111 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>1011101 [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>1011011 [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>1011010 [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>1011001 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>1011000 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>1011000 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>1011000 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>1010111 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>1010101 [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>1010100 [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>1010100 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>1010001 [.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>1010000 [.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,7,5,6,8,4]=>1010000 [.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,8,5,7,6,4]=>1010000 [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>1010000 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>1001111 [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>1001100 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>1001001 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>1001000 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>1001000 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>1001111 [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>1001110 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>1001101 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>1001100 [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>1001001 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>1001001 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>1001000 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>1001000 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>1000110 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>1000101 [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,3,4,2,7,8,6]=>1000100 [.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,3,4,2,8,7,6]=>1000100 [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,4,5,2,8,7]=>1000010 [.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>1000010 [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>1000011 [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>1000011 [.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,3,5,4,2,7,8]=>1000011 [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,6,4,3,5,2,7,8]=>1000011 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>1000001 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>1000001 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,4,5,7,2,8]=>1000001 [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>1000001 [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>1000001 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>1000001 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>1000000 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>1000000 [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,4,5,8,7,2]=>1000000 [.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>1000000 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,8,4,5,6,7,2]=>1000000 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,8,4,6,7,5,2]=>1000000 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,8,5,4,6,7,2]=>1000000 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,8,5,6,7,4,2]=>1000000 [.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,8,5,7,6,4,2]=>1000000 [.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,8,6,5,7,4,2]=>1000000 [.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,7,5,6,4,2]=>1000000 [.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>1000000 [.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>1000000 [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>1000000 [.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,8,5,6,7,2]=>1000000 [.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,8,5,7,6,2]=>1000000 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,8,6,7,5,2]=>1000000 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>1000000 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,3,4,8,6,7,2]=>1000000 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>1000000 [.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>1000000 [.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,6,3,5,4,8,7,2]=>1000000 [.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,6,4,5,3,8,7,2]=>1000000 [.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>1000000 [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7,5,4,3,6,8,2]=>1000000 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,8,3,4,6,7,5,2]=>1000000 [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,8,3,5,6,4,7,2]=>1000000 [.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,8,3,6,5,4,7,2]=>1000000 [.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8,3,5,7,6,4,2]=>1000000 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8,3,7,6,5,4,2]=>1000000 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,8,4,3,5,6,7,2]=>1000000 [.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,8,4,3,5,7,6,2]=>1000000 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8,5,4,3,6,7,2]=>1000000 [.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8,5,4,6,3,7,2]=>1000000 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,8,4,5,6,7,3,2]=>1000000 [.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,8,4,6,5,7,3,2]=>1000000 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,8,4,7,6,5,3,2]=>1000000 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,8,5,4,6,7,3,2]=>1000000 [.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>1000000 [.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,8,6,4,5,7,3,2]=>1000000 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,8,6,5,4,7,3,2]=>1000000 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8,7,5,6,4,3,2]=>1000000 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>1000000 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>0111111 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>0111110 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>0111011 [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>0111010 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>0111000 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,8,6,7,5]=>0111000 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>0111000 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>0110110 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>0110100 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>0110010 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>0110000 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>0101111 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>0101110 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>0101011 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>0101010 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>0101001 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>0101000 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>0101000 [[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>0100110 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>0100010 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>0100011 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>0100010 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>0100000 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>0100000 [[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>0100000 [[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,8,6,5,7,3]=>0100000 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>0100000 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>0100000 [[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,6,4,5,8,7,3]=>0100000 [[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,7,5,6,4,8,3]=>0100000 [[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,8,5,4,6,7,3]=>0100000 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>0100000 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,8,7,5,6,4,3]=>0100000 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>0100000 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>0011111 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0011100 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>0011000 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>0010101 [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>0010010 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>0010001 [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>0010000 [[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>0010000 [[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,8,6,7,5,4]=>0010000 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>0010000 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>0011111 [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>0011100 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>0011100 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>0011001 [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>0011000 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,8,6,7,5]=>0011000 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>0011000 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>0010101 [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>0010011 [[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>0010001 [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>0010001 [[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,7,5,6,4,8]=>0010001 [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>0010000 [[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>0010000 [[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>0010000 [[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,8,6,7,4]=>0010000 [[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>0010000 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>0010000 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>0010000 [[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,7,5,6,8,4]=>0010000 [[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>0010000 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,8,5,6,7,4]=>0010000 [[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,8,5,7,6,4]=>0010000 [[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,8,6,5,7,4]=>0010000 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,8,6,7,5,4]=>0010000 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>0010000 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>0001111 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>0001000 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>0001000 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>0001111 [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>0001000 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>0001000 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>0001111 [[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>0001100 [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>0001011 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>0001010 [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>0001000 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,8,6,7,5]=>0001000 [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>0001000 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7,8]=>0001111 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>0001000 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,2,3,1,8,7,6,5]=>0001000 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>0001111 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>0001110 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>0001101 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>0001100 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>0001100 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>0001011 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>0001010 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>0001001 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>0001001 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>0001000 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>0001000 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>0001000 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,8,6,7,5]=>0001000 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>0001000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>0000111 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>0000100 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>0000111 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>0000100 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>0000111 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>0000101 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>0000100 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,3,4,1,6,7,8]=>0000111 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,3,4,1,8,7,6]=>0000100 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>0000111 [[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>0000110 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>0000100 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>0000111 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>0000100 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>0000111 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>0000110 [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>0000101 [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>0000100 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>0000100 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,2,3,5,1,6,7,8]=>0000111 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,2,3,5,1,7,8,6]=>0000100 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,2,3,5,1,8,7,6]=>0000100 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>0000111 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>0000100 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,2,3,4,1,6,7,8]=>0000111 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,2,3,4,1,8,7,6]=>0000100 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,2,4,3,1,6,7,8]=>0000111 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,2,4,3,1,6,8,7]=>0000110 [[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,4,3,1,7,6,8]=>0000101 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,2,4,3,1,8,7,6]=>0000100 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,3,2,4,1,6,7,8]=>0000111 [[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,3,2,4,1,6,8,7]=>0000110 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3,2,4,1,8,7,6]=>0000100 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,3,4,2,1,6,7,8]=>0000111 [[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3,4,2,1,7,8,6]=>0000100 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3,4,2,1,8,7,6]=>0000100 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>0000111 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>0000110 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>0000101 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>0000100 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>0000100 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,3,5,4,1,8,7]=>0000010 [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,4,5,3,1,7,8]=>0000011 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>0000011 [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,2,4,3,6,1,7,8]=>0000011 [[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2,4,3,6,1,8,7]=>0000010 [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,3,2,4,6,1,7,8]=>0000011 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,3,2,4,6,1,8,7]=>0000010 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>0000011 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>0000010 [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,2,3,5,4,1,7,8]=>0000011 [[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2,3,5,4,1,8,7]=>0000010 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,2,4,5,3,1,7,8]=>0000011 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2,5,4,3,1,8,7]=>0000010 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,3,2,5,4,1,7,8]=>0000011 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>0000010 [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,4,3,2,5,1,7,8]=>0000011 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,4,3,5,2,1,8,7]=>0000010 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,5,3,4,2,1,8,7]=>0000010 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>0000010 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>0000001 [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,5,6,4,1,8]=>0000001 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>0000001 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>0000001 [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,3,4,6,7,1,8]=>0000001 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>0000001 [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,7,3,6,5,4,1,8]=>0000001 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>0000001 [[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>0000001 [[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,7,4,6,5,1,8]=>0000001 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,7,5,6,4,1,8]=>0000001 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>0000001 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,3,7,5,6,1,8]=>0000001 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,2,4,3,7,6,1,8]=>0000001 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,3,4,2,7,6,1,8]=>0000001 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>0000001 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>0000001 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,2,3,4,5,7,1,8]=>0000001 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,2,3,5,4,7,1,8]=>0000001 [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[6,3,2,4,5,7,1,8]=>0000001 [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[6,3,2,5,4,7,1,8]=>0000001 [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[6,3,4,5,2,7,1,8]=>0000001 [[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[6,3,5,4,2,7,1,8]=>0000001 [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,2,3,5,6,4,1,8]=>0000001 [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,6,5,4,1,8]=>0000001 [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,2,4,3,6,5,1,8]=>0000001 [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,2,4,5,3,6,1,8]=>0000001 [[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,2,5,4,3,6,1,8]=>0000001 [[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,6,5,1,8]=>0000001 [[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1,8]=>0000001 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1,8]=>0000001 [[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,3,4,6,5,2,1,8]=>0000001 [[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,5,4,6,2,1,8]=>0000001 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,3,6,4,5,2,1,8]=>0000001 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,3,6,5,4,2,1,8]=>0000001 [[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>0000001 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,6,3,4,5,2,1,8]=>0000001 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,6,4,5,3,2,1,8]=>0000001 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>0000000 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>0000000 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>0000000 [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>0000000 [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>0000000 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>0000000 [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>0000000 [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,4,5,7,8,1]=>0000000 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>0000000 [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,7,4,5,6,8,1]=>0000000 [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,7,4,6,5,8,1]=>0000000 [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,7,5,4,6,8,1]=>0000000 [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,5,6,4,8,1]=>0000000 [[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>0000000 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,4,5,6,7,1]=>0000000 [[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>0000000 [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>0000000 [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>0000000 [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>0000000 [[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,8,6,7,1]=>0000000 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>0000000 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>0000000 [[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>0000000 [[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>0000000 [[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,3,4,8,7,6,1]=>0000000 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>0000000 [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>0000000 [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>0000000 [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,8,6,7,1]=>0000000 [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>0000000 [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,6,3,4,5,7,8,1]=>0000000 [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,6,3,5,4,7,8,1]=>0000000 [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,6,4,3,5,7,8,1]=>0000000 [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,4,5,3,7,8,1]=>0000000 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>0000000 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7,3,5,4,6,8,1]=>0000000 [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,7,3,5,6,4,8,1]=>0000000 [[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,7,5,4,3,6,8,1]=>0000000 [[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,7,5,4,6,3,8,1]=>0000000 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,3,5,7,6,4,1]=>0000000 [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,8,4,3,5,6,7,1]=>0000000 [[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,8,4,3,7,6,5,1]=>0000000 [[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,8,5,4,7,6,3,1]=>0000000 [[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,7,5,4,6,3,1]=>0000000 [[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,7,5,6,4,3,1]=>0000000 [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>0000000 [[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>0000000 [[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>0000000 [[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,7,4,6,5,8,1]=>0000000 [[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,8,5,4,6,7,1]=>0000000 [[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,8,5,7,6,4,1]=>0000000 [[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>0000000 [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,2,3,5,6,8,7,1]=>0000000 [[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,2,3,7,6,5,8,1]=>0000000 [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,3,8,5,6,7,1]=>0000000 [[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,2,3,8,7,6,5,1]=>0000000 [[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>0000000 [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>0000000 [[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>0000000 [[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>0000000 [[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,7,5,6,8,1]=>0000000 [[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>0000000 [[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,8,5,6,7,1]=>0000000 [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,8,6,7,5,1]=>0000000 [[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>0000000 [[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,2,3,4,8,7,6,1]=>0000000 [[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,2,4,3,7,6,8,1]=>0000000 [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>0000000 [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>0000000 [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>0000000 [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,8,6,7,1]=>0000000 [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>0000000 [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>0000000 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>0000000 [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,2,4,3,6,5,8,1]=>0000000 [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,2,4,5,3,6,8,1]=>0000000 [[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,3,4,2,6,5,8,1]=>0000000 [[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,4,3,6,5,2,8,1]=>0000000 [[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8,2,4,7,6,5,3,1]=>0000000 [[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,2,6,4,5,7,3,1]=>0000000 [[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,2,7,5,6,4,3,1]=>0000000 [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8,2,7,6,5,4,3,1]=>0000000 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>0000000 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8,3,2,5,6,4,7,1]=>0000000 [[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>0000000 [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>0000000 [[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,5,3,4,7,6,2,1]=>0000000 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,7,3,6,5,4,2,1]=>0000000 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>0000000 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8,7,5,4,3,6,2,1]=>0000000 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>0000000
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
  • a leaf is associated to the empty Dyck Word
  • a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.