Identifier
Mp00031: Dyck paths to 312-avoiding permutationPermutations
Mp00073: Permutations major-index to inversion-number bijectionPermutations
Mp00069: Permutations complementPermutations
Mp00061: Permutations to increasing tree Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[1,2]=>[2,1]=>[[.,.],.] [1,1,0,0]=>[2,1]=>[2,1]=>[1,2]=>[.,[.,.]] [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,3,1]=>[[.,[.,.]],.] [1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,4,1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[2,4,3,1]=>[[.,[[.,.],.]],.] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[[[[.,.],[[.,.],.]],.],.] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[[[.,.],[[[.,.],.],.]],.] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[[[.,[[.,.],.]],.],[.,.]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[.,[[[[.,.],[.,.]],.],.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[.,[[[.,.],[[.,.],.]],.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[.,[[[.,[.,.]],.],[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[.,[[[.,[.,.]],[.,.]],.]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [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]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [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]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [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]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [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]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [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]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [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]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [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]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [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]=>[6,5,4,2,7,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [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]=>[6,5,4,1,7,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [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]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [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]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [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]=>[5,4,3,1,6,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [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]=>[5,4,3,1,2,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]] [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]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [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]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [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]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [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]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [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]=>[5,4,3,6,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [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]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [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]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [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]=>[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [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]=>[6,5,2,7,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.] [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]=>[6,5,1,7,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]] [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]=>[5,4,1,6,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [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]=>[5,4,2,6,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [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]=>[5,4,1,6,3,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]] [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]=>[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [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]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [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]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [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]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [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]=>[5,4,2,6,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [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]=>[5,4,1,6,7,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]] [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]=>[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [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]=>[5,4,2,3,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [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]=>[5,4,1,3,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]] [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]=>[5,4,1,2,7,6,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [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]=>[4,3,1,2,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [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]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [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]=>[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [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]=>[4,3,1,2,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [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]=>[4,3,1,2,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [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]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [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]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [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]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [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]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [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]=>[5,4,6,3,1,7,2]=>[[[[.,.],[.,.]],.],[[.,.],.]] [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]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [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]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [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]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [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]=>[5,4,6,2,7,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [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]=>[5,4,6,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [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]=>[4,3,5,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [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]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [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]=>[4,3,5,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [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]=>[4,3,5,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [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]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [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]=>[6,4,7,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [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]=>[5,3,6,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]] [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]=>[5,3,6,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [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]=>[5,3,6,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]] [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]=>[4,2,5,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [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]=>[6,3,7,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.] [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]=>[5,2,6,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]] [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]=>[6,2,7,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.] [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]=>[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]] [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]=>[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [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]=>[5,2,6,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.] [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]=>[5,1,6,4,3,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]] [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]=>[5,1,6,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [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]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [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]=>[5,3,6,4,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.] [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]=>[4,2,5,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [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]=>[5,2,6,4,7,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.] [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]=>[5,1,6,4,7,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]] [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]=>[4,1,5,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [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]=>[5,2,6,3,7,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.] [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]=>[5,1,6,3,7,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]] [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]=>[5,1,6,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [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]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [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]=>[4,2,5,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [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]=>[4,1,5,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [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]=>[4,1,5,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [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]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [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]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [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]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [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]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [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]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [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]=>[4,3,5,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [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]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [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]=>[5,3,6,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [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]=>[4,2,5,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [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]=>[5,2,6,7,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.] [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]=>[5,1,6,7,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]] [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]=>[4,1,5,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [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]=>[4,2,5,6,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [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]=>[4,1,5,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [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]=>[4,1,5,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [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]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [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]=>[5,3,4,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [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]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [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]=>[5,2,4,7,6,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.] [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]=>[5,1,4,7,6,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]] [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]=>[4,1,3,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [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]=>[5,2,3,7,6,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.] [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]=>[5,1,3,7,6,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]] [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]=>[5,1,2,7,6,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [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]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [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]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [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]=>[4,1,3,6,5,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [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]=>[4,1,2,6,5,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [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]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [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]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [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]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [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]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [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]=>[4,2,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [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]=>[4,1,5,6,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [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]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [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]=>[4,2,3,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [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]=>[4,1,3,6,7,5,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [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]=>[4,1,2,6,7,5,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [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]=>[3,1,2,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [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]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [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]=>[4,1,3,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [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]=>[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [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]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [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]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [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]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [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]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [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]=>[3,1,2,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [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]=>[3,1,2,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [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]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [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]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.] [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]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [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]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [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]=>[5,6,4,3,1,7,2]=>[[[[.,[.,.]],.],.],[[.,.],.]] [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]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [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]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [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]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [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]=>[5,6,4,2,7,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.] [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]=>[5,6,4,1,7,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [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]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [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]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [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]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [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]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [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]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [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]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [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]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [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]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [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]=>[4,5,3,6,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [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]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [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]=>[5,6,3,7,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.] [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]=>[4,5,2,6,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [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]=>[5,6,2,7,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.] [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]=>[5,6,1,7,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]] [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]=>[4,5,1,6,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [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]=>[4,5,2,6,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [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]=>[4,5,1,6,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [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]=>[4,5,1,6,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [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]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [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]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [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]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [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]=>[4,5,2,6,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [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]=>[4,5,1,6,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [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]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [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]=>[4,5,2,3,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [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]=>[4,5,1,3,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [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]=>[4,5,1,2,7,6,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [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]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [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]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [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]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [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]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [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]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [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]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[5,7,6,4,3,2,1]=>[[[[[.,[[.,.],.]],.],.],.],.] [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]=>[4,6,5,3,2,1,7]=>[[[[.,[[.,.],.]],.],.],[.,.]] [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]=>[4,6,5,3,2,7,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [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]=>[4,6,5,3,1,7,2]=>[[[.,[[.,.],.]],.],[[.,.],.]] [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]=>[3,5,4,2,1,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [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]=>[4,6,5,3,7,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.] [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]=>[3,5,4,2,6,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [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]=>[4,6,5,2,7,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.] [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]=>[4,6,5,1,7,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]] [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]=>[3,5,4,1,6,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [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]=>[3,5,4,2,6,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [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]=>[3,5,4,1,6,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [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]=>[3,5,4,1,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [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]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [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]=>[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.] [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]=>[3,6,5,4,2,1,7]=>[[[.,[[[.,.],.],.]],.],[.,.]] [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]=>[3,6,5,4,2,7,1]=>[[[.,[[[.,.],.],.]],[.,.]],.] [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]=>[3,6,5,4,1,7,2]=>[[.,[[[.,.],.],.]],[[.,.],.]] [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]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [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]=>[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.] [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]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]] [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]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.] [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]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [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]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]] [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]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.] [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]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]] [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]=>[1,6,5,4,2,7,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [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]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [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]=>[3,6,5,4,7,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.] [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]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [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]=>[2,6,5,4,7,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.] [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]=>[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]] [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]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [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]=>[2,6,5,3,7,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.] [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]=>[1,6,5,3,7,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]] [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]=>[1,6,5,2,7,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]] [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]=>[1,5,4,2,6,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [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]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [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]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [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]=>[1,5,4,2,6,7,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [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]=>[1,5,4,2,3,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [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]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [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]=>[4,6,5,7,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.] [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]=>[3,5,4,6,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [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]=>[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [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]=>[3,5,4,6,1,7,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [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]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [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]=>[3,6,5,7,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.] [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]=>[2,5,4,6,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [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]=>[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.] [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]=>[1,6,5,7,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]] [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]=>[1,5,4,6,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [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]=>[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [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]=>[1,5,4,6,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [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]=>[1,5,4,6,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [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]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [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]=>[3,6,4,7,5,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.] [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]=>[2,5,3,6,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [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]=>[2,6,4,7,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.] [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]=>[1,6,4,7,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]] [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]=>[1,5,3,6,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [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]=>[2,6,3,7,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.] [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]=>[1,6,3,7,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]] [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]=>[1,6,2,7,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]] [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]=>[1,5,2,6,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [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]=>[2,5,3,6,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [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]=>[1,5,3,6,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [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]=>[1,5,2,6,4,7,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [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]=>[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [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]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [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]=>[3,5,4,6,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [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]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [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]=>[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [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]=>[1,5,4,6,7,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [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]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [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]=>[2,5,3,6,7,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [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]=>[1,5,3,6,7,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [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]=>[1,5,2,6,7,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [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]=>[1,4,2,5,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [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]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [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]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [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]=>[1,5,2,4,7,6,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [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]=>[1,5,2,3,7,6,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [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]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [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]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [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]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [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]=>[1,4,2,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [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]=>[1,4,2,3,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [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]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [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]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [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]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [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]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [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]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [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]=>[4,5,6,3,1,7,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [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]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [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]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [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]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [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]=>[4,5,6,2,7,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [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]=>[4,5,6,1,7,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [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]=>[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [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]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [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]=>[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [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]=>[3,4,5,1,2,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [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]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.] [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]=>[3,5,6,4,2,1,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [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]=>[3,5,6,4,2,7,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [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]=>[3,5,6,4,1,7,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [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]=>[2,4,5,3,1,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [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]=>[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.] [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]=>[2,5,6,4,3,1,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [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]=>[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.] [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]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,[.,.]],.],.],.],.]] [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]=>[1,5,6,4,3,2,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [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]=>[2,5,6,4,3,7,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [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]=>[1,5,6,4,3,7,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [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]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [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]=>[1,4,5,3,2,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [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]=>[3,5,6,4,7,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [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]=>[2,4,5,3,6,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [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]=>[2,5,6,4,7,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [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]=>[1,5,6,4,7,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [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]=>[1,4,5,3,6,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [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]=>[2,5,6,3,7,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [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]=>[1,5,6,3,7,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [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]=>[1,5,6,2,7,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [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]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [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]=>[2,4,5,3,6,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [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]=>[1,4,5,3,6,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [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]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [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]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [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]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [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]=>[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.] [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]=>[3,4,6,5,2,1,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [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]=>[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [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]=>[3,4,6,5,1,7,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [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]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [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]=>[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.] [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]=>[2,4,6,5,3,1,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [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]=>[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.] [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]=>[1,5,7,6,4,3,2]=>[.,[[[[.,[[.,.],.]],.],.],.]] [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]=>[1,4,6,5,3,2,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [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]=>[2,4,6,5,3,7,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [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]=>[1,4,6,5,3,7,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [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]=>[1,4,6,5,2,7,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [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]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [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]=>[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.] [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]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [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]=>[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.] [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]=>[1,4,7,6,5,3,2]=>[.,[[[.,[[[.,.],.],.]],.],.]] [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]=>[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [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]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.] [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]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]] [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]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [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]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [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]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [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]=>[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [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]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [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]=>[1,2,6,5,3,7,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [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]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [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]=>[3,4,6,5,7,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [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]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [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]=>[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [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]=>[1,4,6,5,7,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [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]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [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]=>[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [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]=>[1,3,6,5,7,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [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]=>[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [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]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [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]=>[2,3,6,4,7,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [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]=>[1,3,6,4,7,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [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]=>[1,2,6,4,7,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [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]=>[1,2,6,3,7,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [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]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [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]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [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]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [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]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [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]=>[1,2,5,3,6,7,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [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]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [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]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [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]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [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]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [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]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [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]=>[3,4,5,6,1,7,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [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]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [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]=>[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [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]=>[2,4,5,6,3,1,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [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]=>[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [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]=>[1,5,6,7,4,3,2]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [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]=>[1,4,5,6,3,2,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [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]=>[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [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]=>[1,4,5,6,3,7,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [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]=>[1,4,5,6,2,7,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [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]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [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]=>[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [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]=>[2,3,5,6,4,1,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [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]=>[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [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]=>[1,4,6,7,5,3,2]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [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]=>[1,3,5,6,4,2,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [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]=>[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [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]=>[1,3,6,7,5,4,2]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [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]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [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]=>[1,2,5,6,4,3,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [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]=>[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [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]=>[1,3,5,6,4,7,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [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]=>[1,2,5,6,4,7,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [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]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [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]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [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]=>[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [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]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [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]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [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]=>[1,4,5,7,6,3,2]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [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]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [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]=>[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [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]=>[1,3,5,7,6,4,2]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [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]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [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]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [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]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [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]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [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]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [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]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [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]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [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]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [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]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [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]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [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]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [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]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [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]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [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]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [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]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [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]=>[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [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]=>[1,4,5,6,7,3,2]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [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]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [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]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [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]=>[1,3,5,6,7,4,2]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [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]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [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]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [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]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [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]=>[1,3,4,6,7,5,2]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [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]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [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]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [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]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [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]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [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]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [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]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [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]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [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]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [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]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [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]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [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]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [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]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [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]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [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]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [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]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [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]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [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]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [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]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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.