Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2Cc0021;cc-rep-3
[1,0]=>[1]=>[.,.]=>[[]] [1,0,1,0]=>[1,2]=>[.,[.,.]]=>[[],[]] [1,1,0,0]=>[2,1]=>[[.,.],.]=>[[[]]] [1,0,1,0,1,0]=>[1,2,3]=>[.,[.,[.,.]]]=>[[],[],[]] [1,0,1,1,0,0]=>[1,3,2]=>[.,[[.,.],.]]=>[[],[[]]] [1,1,0,0,1,0]=>[2,1,3]=>[[.,.],[.,.]]=>[[[]],[]] [1,1,0,1,0,0]=>[2,3,1]=>[[.,.],[.,.]]=>[[[]],[]] [1,1,1,0,0,0]=>[3,2,1]=>[[[.,.],.],.]=>[[[[]]]] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[],[],[],[]] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[[],[],[[]]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[[],[[]],[]] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[[],[[]],[]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[.,[[[.,.],.],.]]=>[[],[[[]]]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[[[]],[],[]] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]]=>[[[]],[[]]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]=>[[[]],[],[]] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]=>[[[]],[],[]] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[[.,.],[[.,.],.]]=>[[[]],[[]]] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[[[[]]],[]] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]]=>[[[[]]],[]] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[[[.,.],.],[.,.]]=>[[[[]]],[]] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[[[[[]]]]] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[],[],[],[],[]] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[],[],[],[[]]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[],[],[[]],[]] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[[],[],[[]],[]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>[[],[],[[[]]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[],[[]],[],[]] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[[],[[]],[[]]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[[],[[]],[],[]] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[[],[[]],[],[]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]=>[[],[[]],[[]]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>[[],[[[]]],[]] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]=>[[],[[[]]],[]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]]=>[[],[[[]]],[]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>[[],[[[[]]]]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[]],[],[],[]] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>[[[]],[],[[]]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>[[[]],[[]],[]] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]=>[[[]],[[]],[]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>[[[]],[[[]]]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[]],[],[],[]] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]=>[[[]],[],[[]]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[]],[],[],[]] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]=>[[[]],[],[],[]] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]=>[[[]],[],[[]]] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]=>[[[]],[[]],[]] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]=>[[[]],[[]],[]] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]=>[[[]],[[]],[]] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]=>[[[]],[[[]]]] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>[[[[]]],[[]]] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]=>[[[[]]],[[]]] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]=>[[[[]]],[],[]] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]]=>[[[[]]],[[]]] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[[[[[]]]],[]] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]=>[[[[[]]]],[]] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]=>[[[[[]]]],[]] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]=>[[[[[]]]],[]] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[[[[[[]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[],[],[],[]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[[],[],[],[],[[]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[],[],[],[[]],[]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[],[],[],[[]],[]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>[[],[],[],[[[]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[]],[],[]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[],[],[[]],[[]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[]],[],[]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[]],[],[]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[],[],[[]],[[]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[]]],[]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[]]],[]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[]]],[]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>[[],[],[[[[]]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[],[[]],[],[],[]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[],[[]],[],[[]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[],[[]],[[]],[]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[],[[]],[[]],[]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[[],[[]],[[[]]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[],[[]],[],[],[]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[],[[]],[],[[]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[],[[]],[],[],[]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[],[[]],[],[],[]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[],[[]],[],[[]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[],[[]],[[]],[]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[],[[]],[[]],[]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[],[[]],[[]],[]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]=>[[],[[]],[[[]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[[],[[[]]],[[]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[[],[[[]]],[[]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[],[[[]]],[],[]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[[],[[[]]],[[]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>[[],[[[[]]]],[]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[[],[[[[]]]],[]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[[],[[[[]]]],[]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[[],[[[[]]]],[]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>[[],[[[[[]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[],[],[]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[[]],[],[],[[]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[]]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[]],[[]],[[]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[]],[[]],[[]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[[[]],[[[[]]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[],[],[]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[[]],[],[],[[]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[]]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[],[],[]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[[]],[],[],[[]]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[],[],[]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[],[],[]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[[]],[],[],[[]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[]],[]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[]],[[]],[[]]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[]],[[]],[[]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[]],[[]],[],[]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[]],[[]],[[]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[]],[[[]]],[]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]=>[[[]],[[[[]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[[[[]]],[[[]]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[[[[]]],[[[]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[]]],[],[],[]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[]]],[],[[]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[]]],[[]],[]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]]=>[[[[]]],[[[]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[[]]]],[[]]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[[]]]],[[]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[[]]]],[[]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[]]]],[],[]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[[]]]],[[]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[[[[[[[]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[],[],[],[],[],[]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[],[],[],[],[],[[]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[],[],[],[[]],[]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[],[],[],[[]],[]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[],[],[],[],[[[]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[],[],[[]],[],[]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[],[],[[]],[[]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[],[],[[]],[],[]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[],[],[[]],[],[]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[],[],[[]],[[]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[],[],[[[]]],[]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[],[],[[[]]],[]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[],[],[[[]]],[]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[],[],[],[[[[]]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[],[[]],[],[],[]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[],[[]],[],[[]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[],[],[[]],[[[]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[],[[]],[],[],[]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[],[[]],[],[[]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[],[[]],[],[],[]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[],[[]],[],[],[]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[],[[]],[],[[]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[],[],[[]],[[[]]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[],[],[[[]]],[[]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[],[],[[[]]],[[]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[],[],[[[]]],[[]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[],[],[[[[]]]],[]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[],[],[[[[]]]],[]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[],[],[[[[]]]],[]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[],[],[[[[]]]],[]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[[],[],[[[[[]]]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[]],[],[],[[]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[]],[],[[[]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[],[[]],[[[[]]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[]],[],[],[[]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[]],[],[[[]]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[]],[],[],[[]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[]],[],[],[[]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[]],[],[[[]]]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[]],[[[]]],[]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[],[[]],[[[[]]]]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[],[[[]]],[[[]]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[],[[[]]],[[[]]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[],[[[]]],[[[]]]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[]]]],[[]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[]]]],[[]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[]]]],[[]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[]]]],[[]]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[[],[[[[[[]]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[]],[],[[[[]]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[[[]],[[[[[]]]]]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[]],[],[[[[]]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[]],[],[[[[]]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[[[]],[[[[[]]]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[]]],[[[[]]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[]]],[[[[]]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[]]],[[[[]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[[]]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[],[],[],[],[],[],[],[]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[],[],[[]],[[]],[],[]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[],[[]],[],[],[[]],[]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[],[[]],[],[[]],[],[]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[],[[[]]],[[[]]],[]] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[]],[],[],[],[],[[]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[]],[[]],[[]],[[]]] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[]],[[]],[[[[]]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[]],[[[[]]]],[[]]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[[]],[[[[[[]]]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[]],[],[],[],[[]],[]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[]],[],[],[[]],[],[]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[]],[[]],[[[]]],[]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[]]],[],[],[[[]]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[]]],[],[[]],[[]]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[]]],[],[[[]]],[]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[[]]]],[[]],[[]]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[[]]]],[[[[]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[[]]]]]],[[]]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[[]]]]]]]]]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
  • if $x$ is the left child of $y$, $x$ becomes the first child of $y$.