Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2
[1,0]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,0,1,0]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,3,1]=>[[.,[.,.]],.] [1,1,1,0,0,0]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[[.,[[.,.],.]],.] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.] [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.] [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[.,[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[.,[[[.,[.,.]],[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[.,[[[[.,.],[.,.]],.],.]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[[.,.],[[[.,[.,.]],.],.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[[.,[[.,[[.,.],.]],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[[.,[[[.,[.,.]],.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[[[.,.],[[.,[.,.]],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[[[.,.],[[[.,.],.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[[[.,[.,.]],[[.,.],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[[[.,[.,[[.,.],.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[[[.,[[.,.],.]],.],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[[[.,[[.,.],.]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[[[.,[[.,.],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[[[[.,.],.],[[.,.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[[[[.,.],[[.,.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,[.,.]],.],.]]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,[[.,[.,.]],.]],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,[.,[.,.]]],.],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,[[.,.],.]],.],.]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,[.,.]],.],.],.]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[.,[[.,.],[[[.,[.,.]],.],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[.,[[.,[.,[[.,[.,.]],.]]],.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[.,[[.,[[.,[.,[.,.]]],.]],.]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[.,[[.,[[.,[[.,.],.]],.]],.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[.,[[.,[[[.,[.,.]],.],.]],.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[.,[[[.,.],[[[.,.],.],.]],.]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[.,[[[.,[.,[.,[.,.]]]],.],.]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[.,[[[.,[.,[[.,.],.]]],.],.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[.,[[[.,[[.,[.,.]],.]],.],.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[.,[[[.,[[[.,.],.],.]],.],.]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],[[.,.],.]],.]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[.,[[[[.,[.,[.,.]]],.],.],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[.,[[[[.,[[.,.],.]],.],.],.]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,[.,.]],.],.],.],.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[[.,.],[[.,[[.,[.,.]],.]],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[[.,.],[[.,[[[.,.],.],.]],.]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[[.,.],[[[.,[[.,.],.]],.],.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],[.,.]],.]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[[.,.],[[[[.,.],[.,.]],.],.]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[[.,.],[[[[.,[.,.]],.],.],.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[[.,[[.,.],[[[.,.],.],.]]],.] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[[[.,.],.],[[[.,[.,.]],.],.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[[[.,.],[[[[.,.],.],.],.]],.] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[[[.,[.,.]],[[[.,.],.],.]],.] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[[[.,[[.,.],.]],[[.,.],.]],.] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[[[.,[[[.,.],.],.]],.],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[[[.,[[[.,.],.],.]],[.,.]],.] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,[.,.]],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],[[[.,.],.],.]],.] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[[[[.,[.,.]],.],[[.,.],.]],.] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[[[[.,[[.,.],.]],.],.],[.,.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],[[.,.],.]],.] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[[[[[.,[[.,.],.]],.],.],.],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
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.