Identifier
Mp00031: Dyck paths to 312-avoiding permutationPermutations
Mp00073: Permutations major-index to inversion-number bijectionPermutations
Mp00061: Permutations to increasing tree Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[[.,[.,.]],.] [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[[.,.],[.,.]] [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[[[.,[.,[.,.]]],.],[.,.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,[[.,.],.]]],[.,.]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[[[.,[.,.]],.],[.,[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[[.,[[.,.],.]],[.,[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[[.,[[.,.],.]],[.,[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[[[.,[[.,.],.]],[.,.]],.] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[[[[.,[.,.]],.],.],[.,.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[[[.,[[.,.],.]],.],[.,.]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[[[.,[[.,.],.]],.],[.,.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[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]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[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]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[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]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[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]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[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]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[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
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.