Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-1Cc0010;cc-rep-3
[1]=>[1,0]=>[1]=>[.,.] [1,1]=>[1,0,1,0]=>[2,1]=>[[.,.],.] [2]=>[1,1,0,0]=>[1,2]=>[.,[.,.]] [1,1,1]=>[1,0,1,0,1,0]=>[2,3,1]=>[[.,[.,.]],.] [1,2]=>[1,0,1,1,0,0]=>[2,1,3]=>[[.,.],[.,.]] [2,1]=>[1,1,0,0,1,0]=>[1,3,2]=>[.,[[.,.],.]] [3]=>[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,3]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [2,2]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [3,1]=>[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [4]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] [1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] [1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] [1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]] [1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]] [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]] [1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]] [1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]] [1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,5,1,6,7,9,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]] [1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]] [1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]] [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]] [1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]] [1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,6,8,9,7]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]] [1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,9,8]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] [1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,8,3,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] [1,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,5,3,6,7,8,9]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] [1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,9,5]=>[[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]] [1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]] [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,9,4]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] [2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,9]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] [2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,7,2,8,9]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]] [2,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,2,6,7,8,9]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]] [2,1,2,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7,9]=>[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]] [2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]] [2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] [2,5,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] [3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,5,3,6,7,8,9]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]] [3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]] [3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,7,8,9,6]=>[.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]] [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] [4,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,8,4,9]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]] [4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]] [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] [6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,6,9]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]] [6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] [1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] [1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,10,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] [1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] [1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,9,10,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]] [1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]] [1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] [1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,10,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]] [1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7,10,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]] [1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] [1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,10,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]] [1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8,10]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],[.,.]]]] [1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,10,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,5,8,9,10,7]=>[[.,[.,[.,.]]],[[.,.],[[.,[.,[.,.]]],.]]] [1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7,10,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]] [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,10,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] [1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] [1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,7,8,3,10,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] [1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,9,10,5]=>[[.,.],[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]] [1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,9,10,7]=>[[.,.],[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]] [1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [1,2,4,1,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,8,9,10,7]=>[[.,.],[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]] [1,5,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,7,8,9,10,6]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] [1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,6,7,9,10,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] [2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] [2,1,7]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9,10]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]] [2,2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,8,6,10,9]=>[.,[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]] [2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] [2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] [2,2,3,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,8,9,10,7]=>[.,[[.,.],[[.,.],[.,[[.,[.,[.,.]]],.]]]]] [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] [3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] [4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] [4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]] [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] [5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] [5,2,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,10,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]] [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] [6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] [6,1,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,9,6,10]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]] [6,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,8,6,9,10]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]] [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] [7,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,9,7,10]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]] [7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]] [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] [1,2,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] [1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.